Before we can consider the crucifixion, we need to understand the bigger picture. Why did God create humans?

The purpose of mankind

According to Paul:

Blessed be the God and Father of our Lord Jesus Christ, who has blessed us in Christ with every spiritual blessing in the heavenly places, even as He chose us in Him before the foundation of the world, that we should be holy and blameless before Him. In love He predestined us for adoption to Himself as sons through Jesus Christ, according to the purpose of His will to the praise of His glorious grace, with which He has blessed us in the Beloved. -- Ephesians 1:3-6 (ESV)

According to a Psalmist:

All nations whom You have made shall come and worship before You, O Lord, and shall glorify Your name. For You are great, and do wondrous things; You alone are God. -- Psalm 86:9-10 (NKJV)

The problem with mankind

Genesis 3 explains how mankind choose to disobey (sin) God's commands and consequently God had to separate Himself form us.

Therefore, just as sin came into the world through one man (Genesis 3), and death through sin, and so death spread to all men because all sinned. -- Romans 5:12 (ESV)

Therefore, mankind is incapable to fulfill their purpose:

For there is no distinction: for all have sinned and fall short of the glory of God. -- Romans 3:22-23 (ESV)

Sin causes division between God and the world:

Behold, the LORD's hand is not shortened, that it cannot save, or His ear dull, that it cannot hear; but your iniquities have made a separation between you and your God, and your sins have hidden His face from you so that he does not hear. -- Isaiah 59:1-2 (ESV)

The solution for mankind

For as by a man came death, by a man has come also the resurrection of the dead.
For as in Adam all die, so also in Christ shall all be made alive.

-- 1 Corinthians 15:21-22 (ESV)

Which means:

We know that our old self was crucified with him in order that the body of sin might be brought to nothing, so that we would no longer be enslaved to sin. For one who has died has been set free from sin.

Now if we have died with Christ, we believe that we will also live with him. We know that Christ, being raised from the dead, will never die again; death no longer has dominion over him. For the death he died he died to sin, once for all, but the life he lives he lives to God.

So you also must consider yourselves dead to sin and alive to God in Christ Jesus.

-- 1 Corinthians 15:6-11 (ESV)

The purpose of the crucifixion

The Pharisees feared that Jesus' growing influence could lead to a perceived coronation as a "new king", triggering a Roman military response and potentially resulting in the destruction of their temple and nation. Ironically, despite crucifying, Jesus, the Romans still destroyed the temple and the nation in 70 AD.

Many of the Jews therefore, who had come with Mary and had seen what he did, believed in him, but some of them went to the Pharisees and told them what Jesus had done.

So the chief priests and the Pharisees gathered the council and said, “What are we to do? For this man performs many signs. If we let him go on like this, everyone will believe in him, and the Romans will come and take away both our place and our nation.”
But one of them, Caiaphas, who was high priest that year, said to them, “You know nothing at all. Nor do you understand that it is better for you that one man should die for the people, not that the whole nation should perish.”

(He did not say this of his own accord, but being high priest that year he prophesied that Jesus would die for the nation, and not for the nation only, but also to gather into one the children of God who are scattered abroad.)

So from that day on they made plans to put him to death.

-- John 11:45-53 (ESV)

From Jesus perspective:

Now as they were eating, Jesus took bread, and after blessing it broke it and gave it to the disciples, and said, “Take, eat; this is my body.” And he took a cup, and when he had given thanks he gave it to them, saying, “Drink of it, all of you, for this is my blood of the covenant, which is poured out for many for the forgiveness of sins. -- Matthew 26:26-28 (ESV)

or

And he took a cup, and when he had given thanks he said, “Take this, and divide it among yourselves. For I tell you that from now on I will not drink of the fruit of the vine until the kingdom of God comes.” And he took bread, and when he had given thanks, he broke it and gave it to them, saying, “This is my body, which is given for you. Do this in remembrance of me.” And likewise the cup after they had eaten, saying, “This cup that is poured out for you is the new covenant in my blood. -- Luke 22:17-20 (ESV)

or

And as they were eating, he took bread, and after blessing it broke it and gave it to them, and said, “Take; this is my body.” And he took a cup, and when he had given thanks he gave it to them, and they all drank of it. And he said to them, “This is my blood of the covenant, which is poured out for many.” -- Mark 14:22-24 (ESV)

Paul explains:

For I received from the Lord what I also delivered to you, that the Lord Jesus on the night when he was betrayed took bread, and when he had given thanks, he broke it, and said, “This is my body which is for you. Do this in remembrance of me.” In the same way also he took the cup, after supper, saying, “This cup is the new covenant in my blood. Do this, as often as you drink it, in remembrance of me.”

For as often as you eat this bread and drink the cup, you proclaim the Lord's death until he comes.

-- 1 Corinthians 11:23-26 (ESV)

These witnesses testify that Jesus had to "pour out" his "blood" to establish the new covenant.

The purpose of the new covenant

For while we were still weak, at the right time Christ died for the ungodly. For one will scarcely die for a righteous person (though perhaps for a good person one would dare even to die) but

1. God shows his love for us in that while we were still sinners, Christ died for us.
2. Since, therefore, we have now been justified by his blood, much more shall we be saved by him from the wrath of God.
3. For if while we were enemies we were reconciled to God by the death of His Son, much more, now that we are reconciled, shall we be saved by his life.
4. More than that, we also rejoice in God through our Lord Jesus Christ, through whom we have now received reconciliation.

-- Romans 5:6-11 (ESV)

Meaning of reconciliation to God

Often people mistakenly think that God can only forgive us if Jesus blood "paid" the penalty of our sin. However, there are many scriptures that state that God forgave people's sin before Jesus was crucified (Isaiah 43:25; Daniel 9:19; Matthew 6:14-15). Even Jesus himself proclaimed that people were forgiven before he was crucified (Mark 2:6-12 (ESV); Matthew 9:2-8).

The Greek word translated as "reconciliation" is "katallássō":

2644 katallássō (from 2596 /katá, "down to an exact point," intensifying 236 /allássō, "to change") – properly, decisively change, as when two parties reconcile when coming ("changing") to the same position.

2644 /katallássō ("decisively changed, reconciled") is applied to marriage partners (1 Corinthians 7:11), but usually in the redemptive sense of a sinner reconciling to the Lord.

[2644 (katallássō) was originally used for the exchange of coins; "properly, to change, exchange (especially of money); hence, of persons, to change from enmity to friendship, to reconcile" (A-S).]

-- HELPS Word-studies

Obviously forgiveness is necessary for reconciliation. However, forgiveness alone only neutralizes the relationship. Reconciliation take it further from "enmity to friendship" or from "divorced" to "married".

It is not okay, to be barely forgiven and saved. The purpose of the new covenant is to establish an intimate fellowship with God which is often compared with a "marriage".

Explanation of the new covenant

And it is needed for this reason:

just as

1. through one man sin entered the world (Romans 5:12) and
2. death through sin, and
3. so death spread to all humankind for all sinned (for sin was in the world before the law, but sin is not charged to one's account when there is no law).

Nevertheless, death reigned from Adam to Moses, even over those who did not sin in a similar way to the transgression of Adam, who is a type of the Coming One. But the free gift is not like the transgression.

Adam	Jesus Christ
For if many died through the transgression of one man, we can be much more certain that	the grace of God and the gift that came by the grace of the one man, Jesus Christ, overflowed to the many.
And the gift is not like what came through the one who sinned. For on the one hand, judgment came from one transgression resulting in condemnation,	but on the other hand, the free gift came after many transgressions resulting in righteousness.
For if by the transgression of the one man, death reigned through that one man,	we can be much more certain that those who receive the overflow of grace and the gift of *righteousness will reign in life through the one man**** -- Jesus Christ.
So then, just as through one transgression the result was condemnation for all people,	so also through one righteous act the result was righteousness that brings life for all people.
For just as through the one man's disobedience the many were made sinners,	so also through the obedience of the one man the many will be made righteous.

-- Romans 5:12-19 (REV)

The result of Adam's transgression is "condemnation" with requires "death". God "paid" for this condemnation by the "death" of His only-begotten son which cost him his blood (life) to enable an alternative outcome: righteousness with God is eternal "life".

For the death that he died, he died to sin once for all;
but the life that he lives, he lives to God.

-- Romans 6:10 (NKJV)

God did not cancel "the reign of death" that Adam established. He provided an alternative. Like Adam and all our ancestors, we still have the option to choose our master and destiny:

Do you not know that if you present yourselves to anyone as obedient slaves, you are slaves of the one whom you obey?

Sin	God
either of sin (trespass), which leads to death,	or of obedience (compliance), which leads to righteousness
But thanks be to God, that you who were once slaves of sin	have become obedient from the heart to the standard of teaching to which you were committed, and, having been set free from sin, have become slaves of righteousness (I am speaking in human terms, because of your natural limitations).
For just as you once presented your members as slaves to impurity and to lawlessness leading to more lawlessness,	so now present your members as slaves to righteousness leading to sanctification.
For when you were slaves of sin, you were free in regard to righteousness. But what fruit were you getting at that time from the things of which you are now ashamed? For the end of those things is death.	But now that you have been set free from sin and have become slaves of God, the fruit you get leads to sanctification and its end, eternal life.
For the wages of sin is death,	but the free gift of God is eternal life in Christ Jesus our Lord.

-- Romans 6:16-23 (ESV)

Jesus was sacrificed to establish a blood covenant. If this covenant did not happen, then we would had to pay with our own blood for our own sin.

Therefore, Jesus blood could also be considered a ransom payment for our sins.

The new covenant prophecy

Isaiah prophesied:

I will make an everlasting covenant with them.
Their offspring shall be known among the nations,
and their descendants in the midst of the peoples;
all who see them shall acknowledge them,
that they are an offspring the LORD has blessed.

-- Isaiah 61:8-9 (ESV)

Then Jesus said that he was fulfilling the prophecy:

And he (Jesus) took a cup, and when he had given thanks he said,

“Take this, and divide it among yourselves. For I tell you that from now on I will not drink of the fruit of the vine until the kingdom of God comes.”

And he took bread, and when he had given thanks, he broke it and gave it to them, saying,

“This is my body, which is given for you. Do this in remembrance of me.”

And likewise the cup after they had eaten, saying,

“This cup that is poured out for you is the new covenant in my blood.

-- Luke 22:17-20 (ESV)

The purpose of the ransom payment

Jesus called them and said... "the Son of Man came not to be served but to serve, and to give his life as a ransom for many." -- Matthew 20:28 (ESV); Mark 10:45

Definition of ransom

the purchasing money for manumitting slaves, a ransom, the price of ransoming; especially the sacrifice by which expiation is effected, an offering of expiation. -- Strong's Concordance

literally, the ransom-money (price) to free a slave -- HELPS Word-studies

λύτρον, λύτρου, τό (λύω), the Sept. passim for כֹּפֶר, גְּאֻלָּה, פִּדְיון, etc.; the price for redeeming, ransom (paid for slaves, Leviticus 19:20; for captives, Isaiah 45:13; for the ransom of a life, Exodus 21:30; Numbers 35:31f) -- Thayer's Greek Lexicon

The aspects of the redemption

In simple terms:

You were ransomed from the futile ways inherited from your forefathers, not with perishable things such as silver or gold, but with the precious blood of Christ, like that of a lamb without blemish or spot. -- 1 Peter 1:18-19 (ESV)

and

He (Jesus Christ) is the propitiation for our sins, and not for ours only but also for the sins of the whole world.

...

In this the love of God was made manifest among us, that God sent his only Son into the world, so that we might live through him. In this is love, not that we have loved God but that He loved us and sent His Son to be the propitiation for our sins.

-- 1 John 2:2,4:9-10 (ESV)

The benefits of this redemption was:

To restore righteousness with God

But now the righteousness (judicial approval) of God has been manifested apart from the law, although the Law and the Prophets bear witness to it — the righteousness (judicial approval) of God through faith (trust) in Jesus Christ for all who believe. For there is no distinction: For all have sinned and fall short of the glory of God, and are justified by His grace as a gift, through the redemption that is in Christ Jesus, whom God put forward as a propitiation by his (Jesus') blood, to be received by faith (trust). This was to show God's righteousness (judicial approval), because in His divine forbearance He had passed over former sins. It was to show His righteousness (judicial approval) at the present time, so that He might be just and the justifier of the one who has faith (trust) in Jesus. -- Romans 3:21-26 (ESV)

Salvation

Salvation is just a side effect of God's reconciliation.

Slaves are to submit to their own masters in all things, doing what is wanted without being argumentative, not pilfering, but showing complete faithfulness in that which is good, so that in all things they make the doctrine of God our Savior attractive. For the grace of God has appeared, bringing salvation for all people, instructing us to deny ungodliness and worldly lusts and to live sensibly and righteously and godly in this present age, while we wait for the blessed hope and appearing of our great God and Savior's glory -- Jesus Christ, who gave himself up for us in order to redeem us from all lawlessness and to cleanse for himself a special people, zealous for good works. -- Titus 2:9-14 (REV)

Adoption by God

God do not just make peace with us. He also adopts believers as his children and makes us heirs of God's promises.

Christ redeemed us from the curse of the law by becoming a curse for us — for it is written,

“Cursed is everyone who is hanged on a tree” -- Deuteronomy 21:23

...

We also, when we were children, were enslaved to the elementary principles of the world. But when the fullness of time had come, God sent forth His Son, born of woman, born under the law, to redeem those who were under the law, so that we might receive adoption as sons. And because you are sons, God has sent the Spirit of his Son into our hearts, crying, “Abba! Father!” So you are no longer a slave, but a son, and if a son, then an heir through God. Formerly, when you did not know God, you were enslaved to those that by nature are not gods. But now that you have come to know God, or rather to be known by God, how can you turn back again to the weak and worthless elementary (beggarly or poor)[https://biblehub.com/greek/4434.htm] principles of the world, whose slaves you want to be once more? -- Galatians 3:13, 4:3-9 (ESV)

and

May you be strengthened with all power, according to his glorious might, for all endurance and patience with joy, giving thanks to the Father, Who has qualified you to share in the inheritance of the saints in light. He has delivered us from the domain of darkness and transferred us to the kingdom of His beloved Son, in whom we have redemption, the forgiveness of sins. -- Colossians 1:11-14 (ESV)

and

In love He (God our Father) predestined us for adoption as sons through Jesus Christ, according to the purpose of His will, to the praise of His glorious grace, with which He has blessed us in the beloved: In him we have redemption through his (the beloved's) blood, the forgiveness of our trespasses, according to the riches of His grace. -- Ephesians 1:7 (ESV)

This payment was not limited to the Jews, but Jesus also paid for the gentiles:

Therefore, remember that at one time you, the Gentiles in the flesh, who are called "uncircumcision" by those who are called "circumcision" (which is done in the flesh by human hands); remember that at that time you were without Christ, excluded from the citizenship of Israel, and strangers to the covenants based on the promise, having no hope and without God in the world.

But now in Christ Jesus you who at one time were far away have been brought near by the blood of Christ. For he is our peace, who made both groups into one and has broken down the dividing wall, the partition between us. He made the hostility (the law consisting of commands expressed in regulations) of no effect by his flesh, so that in himself he could create one new man from the two groups, thus making peace, and so he could reconcile both groups to God in one body by means of the cross, having put to death the hostility by it. And when he came he proclaimed good news of peace to you who were far away and peace to those who were near, 18 because through him we both have access by one spirit to the Father.

So then you are no longer strangers and foreigners, but you are fellow citizens with the holy ones and members of the household of God, having been built on the foundation of the apostles and prophets, Christ Jesus himself being the cornerstone, in whom the whole building, being fitted together, grows into a holy sanctuary in the Lord, in whom you also are being built together by means of the spirit into a dwelling place of God.

-- Ephesians 2:12-22 (REV)

Explanations of the crucifixion

Conclusion

God created us to glorify His authority with our service (worship) and praise.

Sadly, because of our choice to disobey God, we all became sinners condemned to death which seperated us from God so that we are no longer capable to fulfill our purpose.

However, God the Father established a new covenant, with the blood of His son, to restore righteousness to us. Reconciliation would not have been possible without removing the division (cleansing of sin) between God and us. Therefore, the Son of God voluntarily offered himself as hero to provide the way to eternal life with the Father Who loves to adopt us as His children so that we can inherit as fellow heirs with His Son, Jesus Christ, whom He had resurrected like He would also resurrect us one day.

Salvation just happen to be a by-product of God's love for us. It is a gift and not an achievement.

Our purpose and goal should be

1. to live in righteousness with God,
2. serve (worship) Him in love, and
3. testify the truth to others,
4. to the glory of God, and
5. under the authority of our Lord Jesus Christ,
6. which would only be possible if we trust (belief) God with everything,
7. in gratitude for His grace and mercy,

like Jesus demonstrated to us.