Why was Jesus put to death?

The Jews accused Him of blasphemy but didn't have the authority to put Him to death.

Therefore, the Jews accused Him of being a political agitator in hopes that the Romans would do the punishment for them. The Roman leaders could not find fault with Him but it was customary to release a prison at Passover and the Jew's chose another criminal to be released so that Jesus would be executed.

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John 10:33 — 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 {to be} God."

John 5:18 — For this reason therefore the Jews were seeking all the more to kill Him, because He not only was breaking the Sabbath, but also was calling God His own Father, making Himself equal with God.

John 18:31 — So Pilate said to them, "Take Him yourselves, and judge Him according to your law." The Jews said to him, "We are not permitted to put anyone to death,"

Luke 23:2 — And they began to accuse Him, saying, "We found this man misleading our nation and forbidding to pay taxes to Caesar, and saying that He Himself is Christ, a King."

John 18:29-40 — Therefore Pilate went out to them and *said, "What accusation do you bring against this Man?"
They answered and said to him, "If this Man were not an evildoer, we would not have delivered Him to you."
So Pilate said to them, "Take Him yourselves, and judge Him according to your law." The Jews said to him, "We are not permitted to put anyone to death,"
to fulfill the word of Jesus which He spoke, signifying by what kind of death He was about to die.
Therefore Pilate entered again into the Praetorium, and summoned Jesus and said to Him, "Are You the King of the Jews?"