Papal Infallibility

One of the most hotly contested and divisive topics between Catholicism and other sects of Christianity is the authority of the papacy, specifically papal infallibility. Protestant and Orthodox denominations are loath to accept the authority of the Pope, seeing as they deny that Christ created the post at all. We can get to Christ's establishment of the papacy in a later post, but this one just assumes that the pope does have authority as the Vicar of Christ. Even so, there are still some objections to infallibility, most of which result from a misunderstanding of the teaching. For example, some people point out that in Paul's letter to the Galatians, Paul corrects Peter: "But when Cephas came to Antioch I opposed him to his face, because he stood condemned" (Gal 2:11). This, they argue, must mean that Peter, as the Pope, was incorrect and therefore his words are fallible. Others argue that popes disagree about theological teachings, and because two contradictory teachings cannot simultaneously be infallible, the doctrine of infallibility is untrue. However, both of these arguments stem from a misunderstanding of papal infallibility as extending to every word or thought that popes say or think. The Catholic Church defines papal infallibility as:

"The Roman Pontiff, when he speaks ex cathedra, that is, when carrying out the duty of the pastor and teacher of all Christians by virtue of his supreme apostolic authority he defines a doctrine of faith or morals to be held by the universal Church, through the divine assistance promised him in blessed Peter, operates with that infallibility with which the divine Redeemer wished that His church be instructed in defining doctrine on faith and morals; and so such definitions of the Roman Pontiff from himself, but not from the consensus of the Church, are unalterable."

In neither situation in the objections listed above were the popes acting infallibly, or ex cathedra. In context, Paul was correcting Peter and chastising him on his imprudence. Imprudence is definitely not a teaching, much less one given ex cathedra. As for popes having different opinions, infallibility only applies when the pope speaks in union with his bishops or from the Seat of Peter, not when describing his own personal beliefs. So it's very obvious that objections to the doctrine of infallibility can be refuted by correctly understanding the doctrine. 

https://sites.google.com/site/apostolicapologetics/Bishop-of-rome/papal-infallibility#TOC-Objections