Ah, but the Pope when speaking on matters of doctrine is supposed to be infallible.
Of course I accept no pope, and this biblical history of the rebuke of Peter illustrates why very well.
Peter was an apostle, a godly man, but not the head of the church. Jesus is head of the church, and needs no ambassador. Jesus is the Mediator between God and man; there is no Mediator between us and the Mediator.
Jesus knew he wasn’t going to be on earth in person, so he chose Peter as the head of the Apostles, yes, the first Pope.