I think that no one can know exactly for sure, but I would guess that it has something to do with the timing and the socio-political atmosphere that Jesus was in.
In the early part of Jesus’ ministry, He often prevented the demons (who knew who he was and had access to the spiritual realm) to disclose his identity prematurely; perhaps not wanting anyone to worship him before His glorification and His completion of His earthly mission. He however allowed people to slowly draw implications out of his miraculous works and his extraordinary teachings with authority. As times goes on, we see that His claims become more and more explicit; claims that only someone equally divine as the Father can make. Even His opponents after arresting Him, charged Him of claiming himself to be the Son of God, which He could have simply rejected and clarify, and in doing so even save His life; but He went on to say that "But I say to all of you: In the future you will see the Son of Man sitting at the right hand of the Mighty One and coming on the clouds of heaven." (Matthew 26:57-65) Thus, confirming further the charge made against Him.
Once Jesus asked His disciples who they think He was, and eventually Peter answered that He is “the Christ, the Son of the living God” (Matt 16:16) Jesus once again seems to confirm it and even blessed Peter. Maybe Peter got it right even though Jesus had not yet been glorified, while the rest were maybe still not aware. But after that, it puzzles me that He still warned his disciples not to tell anyone that He is the Christ. Perhaps, just perhaps, that just letting his disciples or just Peter to know and get it was enough for Him. Openly proclaiming it to the public would complicate His mission as the public probably still had a wrong conception of what ‘the Christ’, the ‘Saviour’, ‘Messiah’ means. Maybe only after his resurrection would it all be clear and then would everyone know and understand. And by then neither would he need to state anything anymore. They all get it!
