In addressing this issue I'm going to start off with the following question? "Whether or not the Jews are correctly or incorrectly understanding Jesus is not the issue. The issue is what was it that Jesus did or said that caused the Jews to be upset with Him to the point of wanting to kill Him for the specific crime of blasphemy?
You have at John 2:16 Jesus saying, "Take these things away; stop making My Father's house a house of merchandise." At vs18, "The Jews therefore answered and said to Him, "What sign do You show to us, seeing that You do these things?"
Jesus at John 2:19 answers them, "Destroy this temple, and in three days I will raise it up." At vs 20, "The Jews therefore said, "It took forty-six years to build this temple, and will You raise it up in three days?" At vs21 the Apostle John says, "But He was speaking of the temple of His body, referring to His resurrection, vs22.
What's interesting about this exchange/issue is this was brought up three years later at the trial of Jesus. Matthew 26:59-61. They tried to get false testimony against Jesus, in order to put Him to death. At vs61, "This man stated, "I am able to destroy the temple of God and to rebuild it in three days."
Now, getting back to the gospel of John at John 5 Jesus heals a man and the Jews objected because Jesus did it on the Sabbath day. At vs17, Jesus says to them, "My Father is working until now, and I My self am working." Vs18, "For this reason the Jews were seeking all the more to kill Him, because (or why?) He was calling God His own Father, making Himself equal with God."
Jesus also called God His own Father when He was 12 years old at Luke2:49 when His parents were looking for Him. Cutting to the chase the fact is the Jews wanted to kill Jesus for claiming to be God. It's all documented in the trial record at Matthew 26:57-66.
After the John 5:17-18 incident you have Jesus saying at John 8:58, "Truly, truly, I say to you, before Abraham sprang into existence I am." Vs59, "Therefore they picked up stones to throw at Him; but Jesus hid Himself, and went out of the temple."
Now look at John 10:30 where Jesus says, "I and My Father We are one." At vs31 the Jews react, "The Jews took up stones AGAIN to stone Him." Vs32, "Jesus ask, "why are you stoning Me?"
Vs33, "The Jews answered Him. "For a good work we do not stone You, but for blasphemy, and because You, being a man make Yourself out God." There it is, the so-called blasphemy. In John's gospel where Jesus was before Pilate notice, (John 19:6) Pilate says, "Take Him yourselves and crucify Him, for I find no guild in Him." Vs7, "The Jews answered him, "We have a law, and by that law He ought to die because (or why), He made Himself out the Son of God."
The Law the Jews are referencing for blasphemy is at Leviticus 24:16. Getting back to the more extensive trial record is at Matthew 26:57-66. At vs63 the high priest Caiaphas said to Him/Jesus, "I adjure You by the living God, that You tell us whether You are the Christ, the Son of God?"
The high priest is asking Jesus to swear as to His identity. (1), Are you the Christ/Messiah, and (2) the Son of God." At Luke 22:70, Jesus says, "Yes, I am." Here at Matthew 26:65, "Then the high priest tore his robes, saying, "He has blasphemed! What further need do we have of witnesses? Behold, you have now heard the blasphemy;"
Jesus, calling Himself the Son of God is not blasphemy because he really was the Son of God. It would be blasphemy for us to claim to be THE Son of God--as in the (singular) only (there are no others) begotten (uniquely "generated") Son of God, because none of us is really THE SON OF GOD, but Jesus was.
Finally, please notice John 20:3o-31, "Many other signs therefore Jesus also performed in the presence of the disciples, which are not written in this book; vs31, but these have been written that you may believe that Jesus is "the Christ/Messiah, the Son of God; and that believing you may have life in His name."