19 And Pilate wrote a title, and put it on the cross. And the writing was JESUS OF NAZARETH THE KING OF THE JEWS.
20 This title then read many of the Jews: for the place where Jesus was crucified was nigh to the city: and it was written in Hebrew, and Greek, and Latin.
21 Then said the chief priests of the Jews to Pilate, Write not, The King of the Jews; but that he said, I am King of the Jews.
22 Pilate answered, What I have written I have written.
The chief priests appear to be protesting at what Pilates has written, presumably because it appears to be affirming what they wish denied. They ask him write instead that 'he said, I am King of the Jews' - notably they do not ask him to remove the title altogether, or to write a denial.
Why does Pilates affirm what he has written?