Well we know that there was no Papal infallibility in the new church right? That was a later "discovery"
Food for thought:
Remember, in this man Peter, the rock. Hes the one, you see, who on being questioned by the Lord about who the disciples said he was, replied, You are the Christ, the Son of the living God. On hearing this, Jesus said to him, Blessed are you, Simon Bar Jona, because flesh and blood did not reveal it to you, but my Father who is in heaven. And I tell you...You are Peter, Rocky, and on this rock I shall build my Church, and the gates of the underworld will not conquer her. To you shall I give the keys of the kingdom. Whatever you bind on earth shall also be bound in heaven; whatever you loose on earth shall also be loosed in heaven (Mt 16:15 - 19). In Peter, Rocky, we see our attention drawn to the rock. Now the apostle Paul says about the former people, They drank from the spiritual rock that was following them; but the rock was Christ (1 Cor 10:4). So this disciple is called Rocky from the rock, like Christian from Christ.
"Why have I wanted to make this little introduction? In order to suggest to you that in Peter the Church is to be recognized. Christ, you see, built his Church not on a man but on Peters confession. What is Peters confession? You are the Christ, the Son of the living God. Theres the rock for you, theres the foundation, theres where the Church has been built, which the gates of the underworld cannot conquer (John Rotelle, O.S.A., Ed., The Works of Saint Augustine (New Rochelle: New City Press, 1993), Sermons, Volume III/6, Sermon 229P.1, p. 327).