The inscription irritated the Jews.
In Pilate's court they had cried, "Crucify Him." "We have no king but Caesar." John 19:15.
They had declared that whoever should acknowledge any other king was a traitor. Pilate wrote out the sentiment they had expressed. No offense was mentioned, except that Jesus was the King of the Jews. The inscription was a virtual acknowledgment of the allegiance of the Jews to the Roman power. It declared that whoever might claim to be the King of Israel would be judged by them worthy of death. The priests had overreached themselves. When they were plotting the death of Christ, Caiaphas had declared it expedient that one man should die to save the nation. Now their hypocrisy was revealed. In order to destroy Christ, they had been ready to sacrifice even their national existence.
The priests saw what they had done, and asked Pilate to change the inscription. They said, "Write not, The King of the Jews; but that He said, I am King of the Jews." But Pilate was angry with himself because of his former weakness, and he thoroughly despised the jealous and artful priests and rulers. He replied coldly, "What I have written I have written."
Matthew 27:11 discusses Jesus being questioned before the governor and stating that the governor is the one calling him that.
Matthew 27:29 discusses Jesus being mocked by soliders. Matthew 27:38 discusses the sign set over Jesus's head that stated his accusation.