Some people still have the mistaken good Catholics never question the Pope or that we believe that everything the Pope says is infallible. Nothing could be further from the truth. The word infallible is used in the Catholic Church in a very restricted way.
It is centered not in our belief in the Pope but in our belief in the one who founded the Church, Jesus Christ. It is grounded in our belief that even though the Church is made up of all quite fallible, limited human beings, Christ will never allow her to go astray in those matters which are central to the faith. Christ never robs any human being of their free will but, like any good parent, will only let the child learning to walk stray but so far.
In the first reading today Paul says of Peter,
And when Cephas came to Antioch, I opposed him to his face because he clearly was wrong.
But what was he wrong about? Was Peter, the first head of the Church after Jesus's ascension, wrong in what he was preaching? What his teaching incorrect? No.
It was his actions. He was willing to associate with Gentiles, but when his Jewish friends came around, he would fall back into the old ways. By his actions he was promoting the notion that you had to be a Jew to be a real Christian. He fell into the sin of hypocrisy.
The center of the faith for Catholics is not the Pope. The center of the faith for Protestants is not the Bible. The center of the faith for all Christians is the Word of God incarnate, Jesus Christ. The Church, the Pope, the sacraments, the Bible, all other things in our faith share one common purpose to draw us into oneness with him.
Peter was often wrong in the Bible. As we are often wrong. How many times do we fall into the sin of Peter? We know what is right but our friends show up and we want to fit in with them. We don't want them to think we are odd, and so we cave. Peter gives us all hope.