He didn’t. He gave them the “keys” which were symbolic of the keys the Jewish rabbis used to open the storage area for the scrolls which gave them the power and authority to teach Gods word. He also gave them the authority to bind and loose what would be taught in the churches. If someone began to teach something contrary to scripture it was bound and not allowed to be taught.
That might wash if Jesus said the keys to the Word of God, but He didn’t, did He? No, He said, “I will give you the keys of the Kingdom of Heaven.”
Jesus spoke often of the Kingdom of God and the Kingdom of Heaven. Matthew uses Kingdom of Heaven, Luke uses Kingdom of God so it would seem they are the same thing.
First Jesus tells all the Apostles, then He singles out Peter later when He explains why He has changed Simon’s name to “rock”.