And Jesus said unto him, Why callest thou me good? there is none good but one, that is, God. -- Mark 10:18; Luke 18:19; Matthew 19:17 (KJV)

But, Jesus said that he was "good":

"I am the good shepherd..." -- John 10:11,14

Out of context, that would seem like only God can be "good" and Jesus is "good", therefore Jesus has to be God, but that is not was Jesus claimed. There are other scriptures that indicate that other people could also be "good":

A good man out of the good treasure of the heart bringeth forth good things: and an evil man out of the evil treasure bringeth forth evil things. -- Matthew 12:35

That ye may be the children of your Father which is in heaven: for he maketh his sun to rise on the evil and on the good, and sendeth rain on the just and on the unjust. -- Matthew 5-45

So, is Jesus contradicting his own words?

ljthriepland explains:

The word translated as good in the 3 Gospels, used in both the statement of the young man to Jesus and in the reply question of Jesus to the man is the Greek Ἀγαθός, agathos. It means a good nature or to be intrinsically good.

This is NOT the word that Jesus used for himself when he called himself the good shepherd in John 10:11 and John 10:14.

The Greek word translated as good in these verses is Καλός Kalos and means noble, of good character, worthy.

It does not refer to the intrinsic nature of a person.

When Jesus called himself the good shepherd he was referring to him being obedient to God. He did not do his own will but the fathers.

The context in this passage is also very important.

And as he (Jesus) was setting out on his journey, a man ran up and knelt before him and asked him, “Good Teacher, what must I do to inherit eternal life?” -- Mark 10:17; Luke 18:18; Matthew 19:16

Some Bible translators use the words "Good Master" and some "Good Teacher". Either way, Jesus was addressed as a Jewish Rabbi.

ljthriepland explain the context very well. Here is a shortened version of his article:

Rabbis were some of the most respected men in Judaism. They followed the word of God and taught the word of God.

The man had not referred to Jesus as a good person by character rather he called Jesus Good (by nature) teacher. The man had linked being a teacher or rabbi and being by nature good, together. It was to this reference to being called good that Jesus had asked him why he called him good (by nature). Why do you call me good by nature? With the implied question is it because I am a Rabbi? To which Jesus responded that only God was good by nature. In other words don’t think I am good by nature simply because I am a Rabbi. That doesn’t make a person good by nature.

The question posed by Jesus was in response to the question he was asked. He responded to a question with a question. This was something that we see Jesus doing throughout his ministry.

This was actually a very common thing for Rabbis at the time to do, those who have any understanding Of Rabbis and Yeshivas may know exactly what was going on in this conversation.

It was tradition for a person seeking to become a disciple or Yeshiva, to choose a Rabbi to become the disciple of, rather carefully.

...

This particular young man sought out Jesus as Rabbi, seeking an answer to his question regarding inheriting eternal life.

Jesus was now going to show the man that it was not the keeping the commandments or being a Rabbi that made a person good (by nature) as that man had implied. He questioned the man about the commandments, asking him did he know them.

Thou knowest the commandments, Do not commit adultery, Do not kill, Do not steal, Do not bear false witness, Defraud not, Honour thy father and mother -- Mark 10:19

The man replied that he did and importantly to the story, stated that he kept them and had done so from his youth.

And he answered and said unto him, Master, all these have I observed from my youth. -- Mark 10:20

...

The Jews believed that following the commandments and the laws were what made a person good. The man would likely have expected Jesus to have answered that this was how he inherited eternal life. Especially as Jesus had just stated this very thing.

...

The point that Jesus was making thus highlighted. It wasn’t being a Rabbi that made Jesus good (by nature). Through his question why do you call me good (by nature)? He was demonstrating that he was not good (by nature) simply because he was a Rabbi and followed the commandments. the man also followed the commandments but this did not make him by nature good, his true nature was worldly, even though he followed the commandments his nature was not good.

...

Jesus did not say that nobody else but God could be good but that nobody but God was good by nature.

In order to be good by nature we have to become partakers of the divine nature of God.

Whereby are given unto us exceeding great and precious promises: that by these ye might be partakers of the divine nature, having escaped the corruption that is in the world through lust. -- 2 Peter 1:4

Jesus was showing that in order to be (good by nature) a person had to totally change their own nature which was not naturally good and take on the nature of God, and that this was not accomplished by simply following the commandments, or being a Rabbi.