Rome’s doctrine of the infallibility of the pope stems not from the man who occupies the office, but the office itself. God so superintends that teaching office so that regardless of the man, he cannot pronounce error in matters of doctrine and morales (when speaking ex cathedra, and the other numerous qualifications.)
Yet, Paul told Timothy “what you heard from me…entrust to faithful men” (2Ti 2:2). If it were impossible for those in that office to err in those things, why would Paul tell Timothy this? Those who were in the line of Apostolic Succession would be “faithful” (in those things) because of the office, so why would Timothy have to find faithful men?
Also, a brief history of the papacy would reveal that the church did not entrust these things to faithful men, there were many rogues and reprobates in that line. So even if there were such a thing as apostolic succession, the church squandered that long ago. I’m sure the Eastern Church would disagree with that, they’d say that God preserved it through them. That’s another story. And another blog entry. Some other day. Along with the answer of how that works for Protestants. And Baptists.