CathInfo.com

Yes, the popes have corrupted themselves, became modernist heretics and have lost the faith, while at the same time believing they're under the Holy Ghost's protection so whatever they teach can never harm the faithful or the Church, and they are always infallibly safe to follow.

I know, I know - Enter V1's teaching that quotes Our Lord praying that St. Peter not lose the faith....this divine revelation from Our Lord has not been in any way compromised or otherwise infringed upon, because it is a revelation from Our Lord Himself.     this is because Our Lord was referring to when the pope engages his papal infallibility. I cannot remember which if the Fathers taught this, but will look it up when I get the chance, or you can when you get the chance.  

At any rate, as regards the Church's infallibility and indefectibility, words of wisdom.....
"If these two Doctrines be true, then whatever the popes have said or done, whatever they ever say or do, will not be a violation of the Church' s attribute of infallibility. And no matter what anyone does, whether from within or without, he will not succeed in destroying the Church. The enemies of Christ's Church do not believe this, which explains why they will never cease to try". - Fr. Wathen, Who Shall Ascend?

Nonsense? It is a doctrine of the Church, as I already quoted PPXII saying: "The doctrine of the Mystical Body of Christ, which is the Church, was first taught us by the Redeemer Himself" - he was a true pope no?

There are plenty of other authoritative sources as well. Look it up.

There is no contradiction. All of the Church's teachings are infallible whether binding or not, whether defined ex cathedra or not. This is true because Christ is the Church, hence all teachings taught by the Church cannot be anything but truth, which is to say that truth is always infallible. The pope is not the Church, Christ is the Church. The pope is only a man, and outside of when he speaks ex cathedra, can teach errors and all manner or heresy as we've seen since V2 and even before.

When the conciliar popes want us to do or believe heresies or anything that offends God, we cannot accept those teachings because if we do, we offend God. In order to not offend God in this mess, we are first of all under obedience to God, and only then under obedience to man.