John 5:18

This was why the Jews were seeking all the more to kill him, because not only was he breaking the Sabbath, but he was even calling God his own Father, making himself equal with God.

John 5:18

Here in verse 18 we find out that the Jews were seeking to kill Jesus.  The verse goes on to explain the reasons why the Jews were trying to kill him.  The first reason is because he was breaking the Sabbath.  The second reason is because Jesus was calling God his own Father.

Reason 1: "Breaking the Sabbath"

So, how was Jesus breaking the Sabbath in the eyes of the Jews?  Earlier in the chapter we read about an invalid who is healed by Jesus.  While this may have been a miraculous thing, what caught the attention of the Jews was the fact that this happened on the Sabbath.  For some reason, the Jews thought that this was a bad thing and it caused them to persecute Jesus (v16).  In response to their concerns that Jesus was breaking the Sabbath, he provides them with his reasoning in verse 17:

But Jesus answered them, “My Father is working until now, and I am working.”

John 5:17

This issue of the Sabbath comes up multiple times in the gospels and Jesus has differing responses to his critics.  In Luke 13 Jesus responds by calling them hypocrites.  In John 7, referring to this same instance here in John 5, Jesus gives the example of circumcision on the Sabbath and told them to "judge with right judgment".  In Matthew 12, Jesus gives a few examples before telling them "the Son of Man is lord of the Sabbath".  Here in John 5 Jesus provides yet another unique response.

Jesus points to God as the reason why he is doing work on the Sabbath.  Even though God rested on the 7th day of creation and made the Sabbath a day of rest, God couldn't actually take a day off.  In Jewish thought, God still had to keep certain things moving and for him to completely stop would cause many things to stop as well.  Jesus makes the case that since Jesus' father (God) is working even on the Sabbath, it would make sense that Jesus himself would be working as well.  However, the big shocker in this response is the connection that Jesus makes with God.

Reason 2: Calling God his own Father

By calling God his Father, Jesus was not simply calling God "The Father".  He was making a specific connection between him and God.  He was relating to God on a personal level.  By doing so, he made himself "equal with God".  This obviously angered the Jews and made them want to kill Jesus even more than before.

It was blasphemous to make yourself equal with God.  However, it's important to really understand what is meant here.  In this passage, is Jesus equating himself with God?  Though Jesus certainly is God, the context in this particular passage does not necessarily mean the same thing.  Instead, the Jews were outraged that Jesus even put himself on the same level as God by calling God his father.