Why was Jesus condemned for blasphemy by the Jews? Jesus confirmed that He was the Messiah. But this can't be a blasphemy as the Jews were waiting for him.
Jesus confirmed that He was the Son of God. But a lot of people in the old Testament were called Son of God.
Jesus confirmed that He was sitting right next to the Power. Was this the main reason that He committed blasphemy?
The charge of blasphemy in the Gospels, both during Jesus' ministry and in his trial, does not refer to the specific and technical definition of blasphemy, which according to the Mishna, tractate Sanhedrin, Chapter VII, Mishna VI, requires the blasphemer to have mentioned the Name, i.e. the Tetragrammaton, which Jesus never did.  Rather, the charge of blasphemy refers to Jesus' claim of divinity.  Below I present the Gospel passages that show this to be the case both during Jesus' ministry and in his trial.

a. Charges of blasphemy during Jesus' ministry

The meaning of the charge of blasphemy is clear in the very first encounter of Jesus and the scribes recorded in all synoptic Gospels, when Jesus forgives the sins of a paralytic in Capernaum and then heals him:


  And when Jesus saw their faith, he said to the paralytic, "Son, your
  sins are forgiven." 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?" (Mk 2:5-7; also Mt
  9:2-3 and Lk 5:20-21).


In John, the substance of the charge against Jesus is clear in all three occasions when "the Jews", not the Sanhedrin, decided, or actually tried, to kill Him during his ministry. Of these three occasions, only in the third is that charge given a name, which is precisely blasphemy:


  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. (Jn 5:18)
  
  Jesus said to them, "Truly, truly, I say to you, before Abraham was, I
  am." So they picked up stones to throw at him, but Jesus hid himself
  and went out of the temple. (Jn 8:58-59)
  
  (Jesus said) "I and the Father are one." The Jews picked up stones
  again to stone him. Jesus answered them, "I have shown you many good
  works from the Father; for which of them are you going to stone me?"
  The Jews answered him, "It is not for a good work that we are going to
  stone you but for blasphemy, because you, being a man, make yourself
  God." (Jn 10:30-33)


b. Charge of blasphemy in Jesus' trial

I will quote the text in Mark as it is more likely to have greater literal fidelity to the words spoken, as Simon Peter was a direct witness of the trial and Mark composed his Gospel from what he heard from Peter, most probably in Jerusalem in the 40's:


  But he remained silent and made no answer. Again the high priest asked
  him, "Are you the Christ, the Son of the Blessed?" And Jesus said, "I
  am, and you will see the Son of Man seated at the right hand of Power,
  and coming with the clouds of heaven."  And the high priest tore his
  garments and said, "What further witnesses do we need? You have heard
  his blasphemy. What is your decision?" And they all condemned him as
  deserving death. (Mk 14:61-64)


I hypothesize that, while Caiaphas asked his question in Aramaic, Jesus answered in Hebrew, both the "I am" and the following scriptural quote, so that his "I am" was clearly understood by those knowledgeable in the Torah as the "Ehyeh" of Ex 3:14, the Name of God in first person, i.e. when used by God Himself. This would have been an explicit claim of divinity in addition to the one implied in the following combined quote of Psalm 110:1 and Dan 7:13.