There is a difference between 1) contradicting the Magisterium by preaching heresy and 2) defining a doctrine ex cathedra. Per V1, the latter (2) is when he cannot err. This distinction is what the sedes blur and muddy up the waters by morphing popes' ex cathedra definitions into meaning whatever he preaches, essentially extends it to everything he says and does.   

Both sides blunder on the infallibility issue, due to missing the forest for the trees.

R&R types like you effectively gut the indefectibility of the Church by reducing the inerrancy of the Pope and the Church to a handful of once- or twice- per century solemn definitions, whereas you claim the rest can turn to complete crap and total garbage that can't even be recognized as Catholic.

Unfortunately, the SVs counter by exaggerating the scope of infallibility to the point of absurdity, where every time a Pope passes wind (even if it's not from his mouth), he's protected by the Holy Ghost from any shadow of error, where a 2-hour long-winded clearly-speculative speech to a group of midwives or an extremely suspicious docuмent that never even appeared in AAS and was released only in the "Irish Ecclesiastical Review" after the Cardinal who allegedly signed it had died, where both of these might as well have been solemn dogmatic definitions.  While SVs boast of following the pre-V2 "manualists" as if they were practically infallible (an error I refer to as "Cekadism", although Msgr. Fenton excoriated this view as having been promoted by the proto-Modernist Newman), you cannot find a post-V1 and post-V2 theologian who holds such an extreme view of infallibility.  They also exaggerate the notion of "internal assent" to being tantamount to a philosophical assent of the mind even to propositions you believe might be in error, just with a slightly less degree of certainty that the certainty of faith.

Nobody can win this argment, since the SVs have nothing to back up their exaggeration, and yet the R&R minimize to such an extent as to render submission to the Church's Magisterium utterly meaningless, where Stubborn here ends up making himself his own rule of faith.

Msgr. Fenton had a great exposition of the problem with an amazingly nuanced and balanced view of the matter that I urge both sides to look at.

So, the problem can be clarified by focusing correctly on the problem in indefectibility rather than on infallibility.

Let's say that after Vatican II there had been no New Mass, and the only outcome were some ambiguous and a couple erroneous propositions in Vatican II.  Let's say Religious Liberty was the only thing that happened.  No New Mass, no clown Masses, none of this egregious heresy we see today.  There would undoubtedly not have been a Traditional movement, with breakway Trad chapels in hotel rooms on account of a single error or even a handful of errors in V2.

Why?  Because overall the Church would still have been recognizable as essentially Catholic, and theologians would in fact have said, "well, those expository sections in V2 didn't intend to define anything, so they weren't stricly infallible."

But that isn't what we have here, is it?  While one might debate the exact boundary lines between what should be infallble and what should not, clearly the line has been crossed when ...

things are so bad, and the Conciliar Church so substantially different from the pre-V2 Church that had St. Pius X been time-warped forward to our day, he simply would not recognizble.  Essentially, the Conciliar Church lacks the notes of the Catholic Church. +Lefebvre even stated this explicitly on one occasion.

Catholics not only believe they can, but that they even MUST, sever communion with and submission to the putative hierarchy in order to please God and save their souls, where we cannot participate in the same form of Public Worship, what we see as a non-Catholic "Mass" that offends God and harms souls, that we can't accept their catalog of saints, and that we pretty much have to ignore any "teaching" emanating from the Vatican as 95% certain to be filled with Modernism, where even when they get some things right, like blind squirrels or broken clocks, even those things are sure to be pollued by a completely non-Catholic theological framework.

So, the Promises of Christ for the papacy are simply incompatible with this kind of substantial transformation of the Church where we must stay out of it to please God.  Those who say this, even implicitly, are in grave danger of losing their faith.  At that point, hey ... maybe the Prots were right when they said the exact same thing, just figured it out a few hundred years before we did.  Hey, maybe the Old Catholics were right.  So R&R point to only things defined by Vatican I being infallble.  OK, but then what guarantees that the teaching of Vatican I was correct?  Because it met the notes of infallibility?  That would be the ultimately circular reasoning.  Similarly, with the SVs, if they wanted to reject V1 with their principles, they'd simply declare Pius IX an Anti-Pope ... problem solved.

Both sides have serious issues and are unworkable.

Only principles that work are something akin to ... Sede-Doubtism, Sede-Privationism, Sede-Impundism (Chazal's variant), and most importantly, all of them founded upon the principle of DOGMATIC INDEFECTIBILISM.  Whatever the status of the current papal claimant, we cannot attribute this substantial change of the Church to the exercise of legitimate papal authority without that being tantamount to your belief in a defectible Church.

Archbishop Lefebvre actually agreed with this, the SV "major", that the Holy Ghost protects the papacy to prevent this degree of destruction.  He says, "yes, I agree with you."  Sadly, because he did not articulate this emphatically enough, he left a legacy of R&R types here, a gaggle of them, who deny this most basic and fundamental tenet of Catholicism, that the Pope is the anchor of the true faith, as established by Christ.  +Lefebvre, however affirmed this.

Then how is it that he did not become sedevacantist.  He went on to explain in the same talk.  While he agrees with the PRINCIPLE of the SVs, and does in fact state that, yes, SV is a very possible explanation for how all this came about ... he can't fully commit to an explanation of HOW this all happened.

SVs forget that in addition to the "MAJOR" of their syllogism of the Crisis, that there are numerous Minors also involved, and those are not certain with the certainty of faith, and therefore the conclusion of SVism also cannot be dogmatically certain.

+Lefebvre speculates ... in addition to saying that SVism is possible that ... could Montini have been drugged, or kidnapped, or held prisoner, or acting under duress, etc?  He did not think so.  But an "I do not think so" was not sufficient for him to embrace SVism completely, and he deferred to the judgment of the Church.

Let's say I held the opinion that the See was not vacant.  Am I a heretic, per dogmatic SVs?  Yes, they would say I'm a heretic.  But ... wait.  What if I hold that Montini was the true Pope, just that he was kidnapped, drugged, tied up in a Vatican dungeon and replaced by a big-eared, crooked-nosed double who, with a bit of plastic surgery, looked enough like the real Montini to fool everyone.  To paraphrase the pope song ... "You may be right.  I may be crazy.  But it might not be a heretic you're looking at ..."  In order words, even if I'm nuts, I'm not a heretic.  Why?  Because I do not deny the MAJOR of the SV proposition, which is what's certain with the certainty of faith.  I manage to reject the conclusion by denying your MINOR, namely, that the Pope taught error to the Church, since the actual pope was in the dungeon.

Early in SSPX, the mantra repeated by Fr. Schmidberger and others was "melior est conditio possidentis", that the occupants of the office get the "benefit of the doubt" (in the practical order).  That of course presumes doubt.

Here's the thing, folks, you R&R types.  Theologians generally hold that the legitimacy of the Pope is a "dogmatic fact", i.e. that it must be accepted and known with the cetainty of faith, and that if this is not the case, where there's well-founded doubt, that a "doubtful pope is no pope" (at least for all practical intents and purposes).  So when we have +Lefebvre, +Tissier, and +Williamson at different times say that, well, yes, it's possible that these men were not popes, recalling that papal legitimacy is classified as dogmatic fact, if these Popes were in fact legitimate with that certainty of faith ... doubting a dogma or dogmatic fact is the same thing as denying it.  You can neither deny nor doubt something that is required to be held with the certainty of faith, such as a dogmatic fact.

Consequently, +Lefebvre, +Tissier, +Williamson (never heard a peep out of +Galaretta myself) ... are NOT SEDEPLENISTS.  They are SEDE-DOUBTISTS.  Period.

Both sides blunder on the infallibility issue, due to missing the forest for the trees.

R&R types like you effectively gut the indefectibility of the Church by reducing the inerrancy of the Pope and the Church to a handful of once- or twice- per century solemn definitions, whereas you claim the rest can turn to complete crap and total garbage that can't even be recognized as Catholic.

Your problems are too numerous to list, a few are that you doubt the Church's indefectibility, and you've abandoned the meaning of the defined dogma of papal infallibility under the pretext or in the name of a more profound understanding.    

Your problems are too numerous to list, a few are that you doubt the Church's indefectibility, and you've abandoned the meaning of the defined dogma of papal infallibility under the pretext or in the name of a more profound understanding.   

And yet you can't even list them.  You're a pertinacious heretic, Stubborn.  I have repeatedly given you outs so that you can actually cling with white knuckles to the fact that Prevost might be your pope ... without sliding into heresy.  But you absolutely pertinaciously hold to the heresy that the Catholic Church can defect.  You're a non-Catholic who needs to be refused the Sacraments at whatever chapel you attend until you make a public abjuration of your heresy.

You're also a blithering idiot, where your thick skull is impervious to basic logic, and, as it's been pointed out to you, at no point did Vatican I define that, outside of these strict limits, the entirely of the Magisterium can turn to crap, and lead souls to Hell.  There's no such definition that your heretically-perverted and apostate brain keeps trying to inject into it.  So, on the contray, it's you who are making up dogma.

And yet you can't even list them.  You're a pertinacious heretic, Stubborn.  I have repeatedly given you outs so that you can actually cling with white knuckles to the fact that Prevost might be your pope ... without sliding into heresy.  But you absolutely pertinaciously hold to the heresy that the Catholic Church can defect.  You're a non-Catholic who needs to be refused the Sacraments at whatever chapel you attend until you make a public abjuration of your heresy.

You're also a blithering idiot, where your thick skull is impervious to basic logic, and, as it's been pointed out to you, at no point did Vatican I define that, outside of these strict limits, the entirely of the Magisterium can turn to crap, and lead souls to Hell.  There's no such definition that your heretically-perverted and apostate brain keeps trying to inject into it.  So, on the contray, it's you who are making up dogma.

This is the open, obstinate, and uncharitable railing of a man who has cast aside the Catholic duty of fraternal correction and fallen into prideful invective, the sin of contumely joined to rash judgment and uncanonical denunciation, conduct long condemned by traditional Catholic moral theology and wholly foreign to the spirit of one who seeks the salvation of his brother.

Sorry Stubborn, this is false. Please cite an authority who says that those are the only two ways that a pope can lose his office. I can give you several authorities that contradict your claim, but just this one by Father Doyle will do:

That's his opinion.