God does. That’s the point. The Catholic belief, which is written into the very doctrine and dogma of the religion, is that God is guiding the process and that God chooses the Pope. The whole religion is based on the idea that Jesus took the wheel and handed it to Peter afterwards who then handed it to the next person. Papal infallibility, as a concept, is the promise that the leadership of the Catholic Church is free from human error so, yes, according to their own beliefs, they are explicitly immune from that.
God does.
And that’s why this is entirely a circular and nonsensical thing.
Of course it is. But you’re the one arguing against your definition of these terms, not their own. From a standpoint of furthering discussion, I’m an atheist. I don’t believe any of this. But I know what the religion dictates as the definition of who they are and, based on that, you’re wrong about how they view themselves and how they’ve defined themselves.
Again, history is written by the victors. It “just so happens” that the Pope is the Pope because the portion of the Catholic Church which says he’s the Pope has the social, economic, and political power to make that “true.” Which would be the case no matter which portion achieved that set of powers; we could just as easily be referring to a whole different set of Popes, past and present.
I’m not talking about how they view or define themselves. If Catholic dogma wants to say that that’s what God intended, that’s fine. Neither of us has to believe it. If some other set of Popes ended up existing, that would have been “what God intended.”