Some argue that only God can forgive sin. Jesus however, did forgive sin. Therefore, some argue this proof that Jesus must be God.

This was also what the scribes believed:

Now some of the scribes were sitting there, questioning in their hearts, “Why does this man speak like that? He is blaspheming! Who can forgive sins but God alone?”
And immediately Jesus, perceiving in his spirit that they thus questioned within themselves, said to them, “Why do you question these things in your hearts? Which is easier, to say to the paralytic, ‘Your sins are forgiven,’ or to say, ‘Rise, take up your bed and walk’? But that you may know that the Son of Man has authority on earth to forgive sins”.
He said to the paralytic: “I say to you, rise, pick up your bed, and go home.”

And he rose and immediately picked up his bed and went out before them all, so that they were all amazed and glorified God, saying, “We never saw anything like this!”

-- Mark 2:6-12 (ESV); Matthew 9:2-8

At that point in time Jesus have not told or implied that he was God, otherwise the scribes would have rather questioned that view, but instead they questioned how Jesus could forgive sin.

It was the scribes assumption that only God can forgive sin.

Jesus could have responded to the scribes accusation: "But I AM God!", but instead he correct them:

"But that you may know that the Son of Man has authority on earth to forgive sins." -- Mark 2:10

This is also how the crowd understood Jesus:

And he rose and went home. When the crowds saw it, they were afraid, and they glorified God, Who had given such authority to men. -- Matthew 9:8 (ESV)

If the crowd believed that Jesus was God in the flesh, they would not have been "amazed" that Jesus could do miracles in their sight.

After Jesus did his miracle, the Jews "glorified God" instead of Jesus.

If Jesus just proofed that he was God, then the crowed would have reacted differently. When people realized that they were facing God or a heavenly being, they were often scared, tried to hide or fell down and worshipped God, for example:

• Abraham (Genesis 18:1-3)
• Moses (Exodus 3:1-6)
• Israelites (Exodus 20:18-19)
• Isaiah (Isaiah 6:1-5)
• Josua (Josua 5:14)
• Daniel (Daniel 8:16-18)
• John (Revelation 19:9-10, 22:8-9)

Yet in the next few verses (Mark 2:13-17) we read that the crowed did not fear Jesus and continued to approach him as a teacher. Even after this miracle there were no recordings of anyone worshiping Jesus as their God or bringing offerings to Jesus.

If Jesus taught this crowd that he was God, then the scribes would have accused him so at his trail.

Jesus could make this claim because there are evidence that God can delegate this authority to whomever He wishes:

And I said: “Woe is me! For I am lost; for I am a man of unclean lips, and I dwell in the midst of a people of unclean lips; for my eyes have seen the King, the LORD of hosts!”

Then one of the seraphim flew to me, having in his hand a burning coal that he had taken with tongs from the altar.

And he touched my mouth and said: “Behold, this has touched your lips; your guilt is taken away, and your sin atoned for.”

-- Isaiah 6:5-7 (ESV)

and

Then he showed me Joshua the high priest standing before the angel of the LORD, and Satan standing at his right hand to accuse him.

And the LORD said to Satan, “The LORD rebuke you, O Satan! The LORD who has chosen Jerusalem rebuke you! Is not this a brand plucked from the fire?”

Now Joshua was standing before the angel, clothed with filthy garments.

And the angel said to those who were standing before him, “Remove the filthy garments from him.” And to him he said, “Behold, I have taken your iniquity away from you, and I will clothe you with pure vestments.”

-- Zechariah 3:1-4 (ESV)

Even Jesus himself delegated this authority to his disciples:

Jesus said to them again, “Peace be with you. As the Father has sent me, even so I am sending you.”
And when he had said this, he breathed on them and said to them,

“Receive the Holy Spirit. If you forgive the sins of any, they are forgiven them; if you withhold forgiveness from any, it is withheld.”

-- John 20:21-23 (ESV)