**Bottom line here is a simple summary of the Holy Father, the pope, the Bishop of Rome, as the successor to Peter and the Vicar of Christ, when he speaks as the universal teacher from the Chair of Peter in defining faith and morals does so with an infallible charism or an infallible gift through the Holy Spirit so that we can give to him the full assent of our intellect and our will, and we can hear the voice of Christ coming to us through the voice of the pope when he is speaking in this capacity.
We must begin by showing that Jesus conferred this gift upon Peter. Secondly, we have to establish the doctrines of papal succession.
If we can prove from the bible that Peter was granted by Jesus a certain primacy, that doesn’t go far enough. We then have to go on to establish papal succession; that is Peter had successors to whom would be entrusted the same gift or charism. Then thirdly, we have to establish evidence, for papal infallibility, that is that God grants a gift to the successors of Peter for them, not to give new revelations.
The church insists that no popes have ever given new revelation. Revelation has been once and for all deposited by Christ through his apostles and with the death of the last apostle came the close of all public revelation. So that third doctrine is the doctrine of papal infallibility, that when they transmit, when they explain, when they enforce it, they are granted a charism or a special spiritual gift preserving them from error.
It doesn’t mean he always says the right thing, it’s always the right time; but that when he speaks with the authority that Christ gives to him, we have this Divine guarantee, because Christ promises that “I will build my church”.
The church of Christ is not a human institution first and foremost. Jesus identifies it as his own. “My church” and the institution and edification and up building of the church Jesus claims for himself. “I will build my church”.
In Matthew 16, the gates of hell will not prevail against the church, and will not prevail against the Rock which is Peter and the popes who are in the line of succession with Peter.