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There is in fact a role for private judgment where it comes to faith, and it was clearly taught by Vatican I.

It's in determining in the first place the credibility of the authority behind the Magisterium.  We use our reason to assess what are called the "motives of credibility" and to make the determination based on these that the Catholic Church is the True Church founded by Christ that exercises His teaching authority.  We then submit to the authority of the Church's Magisterium.

Where it comes to the Conciliar Church, we see an institution masquerading as the Catholic Church but lacking the notes of the One True Church that is in possession of the teaching authority given to the Church by Our Lord and constantly guided by the Holy Spirit.

We do not recognize the Voice of the Shepherd in Bergoglio, but have discerned the voice of a wolf in sheep's clothing.  Those words of Our Lord couldn't more aptly describe the V2 papal claimants.  These are wolves that have put sheepskins on themselves (the external trappings of the office).

Once we recognize, however, that "yes, this institution here teaches with the teaching authority of Christ," at that point  we submit to it ... not that there can't be some mistakes or imprudences here or there, but it simply cannot go substantially corrupt where submission to its teaching harms our faith.

If this were a matter of simply one or two questionable statements in Vatican II, there would be no Traditional movement.  Instead, people would simply have respectfully disagreed with those statements and pursued a correction within the Church (that's precisely +Schneider's attitude).  Were it not for a radical transformation of the Church at every level, in the Church's publish worship, in the corruption of the catalogue of saints, in 60+ years now of Papal Magisterium that's thoroughly imbued with Modernism, nobody would have severed communion with the Catholic Church.  In fact, the pretty much all of the even-conservative bishops at Vatican II signed most of the V2 docuмents.  It wasn't until the aftermath, in particular, with the imposition of the NOM, that the Traditional movement began to grow.

I doubt that anyone here became a Traditional Catholic by reading/studying the docuмents of Vatican II.  Vast majority of Catholics never read Vatican II.

I do not know how many times this needs to be re-explained to you.  What part of the concept that the V2 Magisterium is not the Catholic Magisterium cannot penetrate the dark recesses of your skull?  At no point has the Magisterium  gone off the rails.

There is no V2 magisterium - such a thing does not even exist. This is the same non-existent magisterium you insist went off the rails, pretty absurd imo.

 The only magisterium is the Catholic Church's magisterium - which, as your papal quotes teach, is unable to be mistaken and always immune from error. It's not complicated.