We haven’t looked at a “tough question” in a while. Let’s continue tackling papal infallibility with: “How can a group of fallible men elect a fallible man as their leader who then becomes infallible through the election?”
We know of many things Peter said and did wrong. (Can you imagine how he might have felt, reading one of the Gospels? “Hey, Matt, did you have to put that in there?”) None of these are infallible, by far.
Look closely at Matt 16:15-17:
He said to them, "But who do you say that I am?" Simon Peter said in reply, "You are the Messiah, the Son of the living God." Jesus said to him in reply, "Blessed are you, Simon son of Jonah. For flesh and blood has not revealed this to you, but my heavenly Father.
Peter’s belief in Jesus didn’t come from man – didn’t originate in man – it came as a revelation from God the Father, from heaven. The truth Peter spoke here, he spoke because God revealed that truth to him.
(It’s worth noting 2 Peter 1:21, also: “For no prophecy ever came through human will; but rather human beings moved by the Holy Spirit spoke under the influence of God.”)
Our trust in papal infallibility comes not from trust in the greatness of men but in the greatness of God. Papal infallibility comes naturally from a belief that God meant what was said in the next few verses of the Gospel of Matthew:
“And so I say to you, you are Peter, and upon this rock I will build my church, and the gates of the netherworld shall not prevail against it. I will give you the keys to the kingdom of heaven. Whatever you bind on earth shall be bound in heaven; and whatever you loose on earth shall be loosed in heaven.” (Matt 16:18-19)
“[T]he gates of the netherworld shall not prevail against [my church].”
If the pope taught something as divinely revealed truth, as an integral part of Catholic faith, that was false, then Jesus’ statement above is a lie. If false teachings have become part of the church, then the great purveyor of lies – Satan – has prevailed against it.
If we believe Jesus’ words, then we must believe that He backs them up, that He will prevent anything other than Truth from becoming part of His Church.
We know Peter made lots of mistakes and said lots of things that were wrong, but these were his personal mistakes and opinions. Peter, any subsequent pope, or any other bishop, can make as few or many mistakes as they happen to make; that has nothing to do with infallibility. Infallability, again, is a faith in God’s power, not in men’s. We believe that if something is stated as part of official Church doctrine, by someone with the authority to do so, then it must be true because God would not allow it to be otherwise.