How do you make sense of the doctrine of the infallibility of the pope? Well, I guess you could start by observing that actually there is a Protestant doctrine which will make a perfect correspondence for it, that is the doctrine of the infallibility of the Scriptures. It boils down to the question of the locus of authority in the church. Where does the authority of Christ lies? Where is it exercised?
(Hence, it is not on whether the pope can’t say anything wrong at all. If I remembered correctly, the current pope himself in the book Light of the World admits that he can be mistaken at times.)