Jesus did not hide His identity. He was the King, He is the King and He will always be the King. The job of a king is to rule; not just to claim territory, but to direct the way people live. So, because Jesus is King, He has the right to tell people how to live and who to worship; and He always tells the truth.
Although Pilate was the highest authority in Israel, Jesus was higher than him. Pilate thought that Jesus should listen to him, but he was wrong. If Pilate had been interested in the truth, he would have done less talking and much more listening.