There were three accusations brought against Jesus;
Firstly that he had threatened to destroy the temple, (Matthew 26:61) Secondly that he claimed to be the son of God, (Matthew 26:63-64) Thirdly that he stirred up the people against Caesar. (John 19:12)
The claim that Jesus had said he could destroy and rebuild the temple in three days was considered to be a fanciful and wholly impossible thing for Jesus to do. Because this wasn't taken seriously, this wasn't taken any further. No-one seemed to understand the spiritual implication to these words of Jesus when applied to his bodily temple, his death and resurrection after three days.
The accusation that Jesus claimed to be the Son of God was the the statement on which his death warrant (by the Jews) was finally signed and quite simply because Jesus admitted to this charge. The High Priest asked him in Matthew 26:63-64 to answer the charge under oath and Jesus as a law abiding citizen, had no choice but to answer. How ironic that Jesus was finally committed to death, not with the aid of false witnesses, but by the words of truth from his own mouth.
The Jews were not allowed to put anyone to death without the permission of the Romans, so another charge was needed, because the Romans were not concerned about matters relating to the Jewish religion. To say that Jesus claimed to be a king would have been taken seriously by the Romans as a threat to Caesar. Once again Jesus had to give them words they could use against him.
So, who was responsible for the arrest of Jesus? Matthew 26:47 tells us that "...a large crowd armed with swords and clubs...... from the chief priests and the elders of the people" came into the garden to arrest Jesus. It is also the chief priests and the elders that moved among the crowds inciting the people to call for the release of Barabbas in Matthew 27:20. Pilate, in fact, actually washed his hands of the trial of this "just man", Matthew 27:24.
The Apostle Peter in Acts 5:30 makes it very clear when talking to the High Priest in Jerusalem that the Jews killed Jesus, "The God of our fathers raised Jesus from the dead -- whom you had killed by hanging on a tree."