The simplest way that I can think of to express the Catholic argument is this:

The pope is infallible because he is the heir of the Apostle Peter’s infallibility.

Roman Catholic doctrine teaches that Christ assigned Peter supreme human authority over the Church, and placed a spiritual safeguard over him to ensure he successfully carried out this leadership assignment. When Peter died, his spiritually-guarded leadership role transferred to a successor, the bishop of Rome (the pope).

There are the four pieces to this argument:

Christ assigned Peter supreme authority over the Church.

This is the first Scripture verse most Catholics will turn to in this discussion:

“You are Peter, and on this rock I will build my church, and the gates of hell will not overpower it. I will give you the keys of the kingdom of heaven. Whatever you bind on earth will have been bound in heaven, and whatever you release on earth will have been released in heaven.” (Matt 16:18)

Catholics say that through a play on the sounds of the word rock (petra) and Peter’s name (petros), Christ promised to build his Church on Peter. Thus, Peter is the foundation of the Church, and as the foundation, Peter held an extra measure of authority among the apostles. Other passages that in one way or another suggest Peter’s supremacy include John 21:15-17; Luke 22.31-32; Matthew 10.2; Acts 1.15; and others.

God placed a spiritual safeguard over Peter to ensure he successfully carried out his leadership assignment.

Catholics argue it like this: Christ promised hell would not prevail over the Church. For that promise to be fulfilled, the Church must remain doctrinally pure. Peter is the foundation of the Church, so he must remain doctrinally pure. Therefore, God must have ensured by supernatural means that Peter remained doctrinally pure for the Church to remain doctrinally pure, too.

Catholics may point to this verse as evidence that Christ prayed for Peter to remain steadfast in his faith, and what Jesus prays for happens:

“Simon, Simon, behold, Satan demanded to have you, that he might sift you like wheat, but I have prayed for you, Simon, that your faith may not fail. When you have turned back, strengthen your brothers.” (Lk 22.31-32)

Peter’s supreme authority, along with the spiritual safeguard, transferred to a successor when he died.

The bishop of Rome (the pope) is the legitimate successor of that spiritually safeguarded authority.

Neither of these two last points are biblically defensible. Neither, however, does Scripture specifically deny their possibilities. It simply doesn’t say anything about them. So since Scripture is silent, Roman Catholics turn to the records of Church history to develop support for these final two points in their argument. They argue that Peter was the first bishop of Rome, and so accordingly, thereafter the bishop of Rome is to always be the foundational safeguarded human authority in the Church.

That−as best as I can tell−is why Roman Catholics believe the doctrine of papal infallibility. From my perspective, Christ does seem to assign Peter a preeminence of some kind, though I’m not sure what that meant to involve. But the argument that Peter was given spiritually-guarded infallibility doesn’t even bounce once for me. I haven’t found any Scripture taken in context that supports the idea. It appears to ultimately derive from a logical argument — the same sort of which was used hundreds of years ago to defend a geocentric solar system. As for the succession of Peter’s authority, I don’t even hear a whisper of it in the Bible. Besides, Peter surely held other posts in his ministry before he settled in Rome. Why shouldn’t the successors of those ministries claim Peter’s authority, too? I am open to all four pieces of the Roman Catholic reasoning for papal preeminence and infallibility being true. But to date I have not seen good evidence.

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The doctrine, itself, can be confusing. So since I was already researching it, this is what the doctrine does and does not mean:

The doctrine of papal infallibility does not teach that a pope is infallible on all matters at every moment. Three conditions must be in place before any papal declaration can be considered infallible:

First, the pope must be specifically intending to declare an infallible statement.

This is called speaking ex cathedra. This term is Latin and means “from the chair.” It refers to the Catholic belief that the pope sits as the highest overseer—the senior pastor—to all Christians in the world. Only when the pope is consciously exercising this authority can a declaration begin to be considered infallible.

Second, the issue the pope is speaking on must regard faith or morals.

Whatever the pope’s opinions are on scientific matters, for instance, remain an issue of personal judgment. Likewise, when the pope looks out the window and says, “What a dreary day!” that doesn’t make it a dreary day for all Christians everywhere.

Third, the pope must be giving information or instruction he intends all Christians everywhere to believe or obey.

The declaration, then, must be relevant to the entire Church; the pope may tell a certain bishop to do something without intending every Christian in the world to do the same thing.

The doctrine of papal infallibility does not teach that the pope is sinless. In his personal life he’s a human fumbling around like the rest of us in desperate need of God’s help to live a holy life. But when he as the universal overseer of the Church speaks or writes something he intends all Christians everywhere to believe or obey, the Holy Spirit preserves him from making any error in judgment or statement.

Other useful information:

The infallibility of the pope was formally defined as an infallible doctrine in 1870 by the First Vatican Council. The belief as a tradition, however, goes back several hundred years earlier. Notice here that a council can also speak infallibly in Roman Catholicism. Any definition by an ecumenical council that is approved by the Pope, concerns faith or morals, and is intended for the whole Church to believe or obey is, in the Roman Catholic’s opinion, infallible.

Because the definition of infallibility is so late in Roman Catholic history, there is no consensus on how often the popes have spoken infallibly. Modern day infallible declarations by both popes and councils, however, are documented carefully. The most recent occurrence was in 1950 when Pope Pius XII declared that the Virgin Mary was transported to Heaven with her body and soul united.

The doctrine of papal infallibility is defined dogma in Roman Catholicism. This means that no one who doubts or denies the teaching can be Catholic. Any Catholic who does not affirm the teaching is a heretic.

More information on: papal infallibility; ecumenical council infallibility; Assumption of Mary; a Roman Catholic explanation and defense of the Doctrine of Infallibility. The picture is of Pope Gregory I by Carlo Saraceni (c. 1610). Note the dove (representing the Holy Spirit) landing on the pope as he writes.