Traditional Catholics generally become Traditional Catholics not because they analyze specific teachings of Vatican II and determine that they're in error. They become Traditional Catholics because their sensus Catholicus tells them that the Conciliar Church is something substantially different than the Catholic Church. I've done this thought experiment before. Let's say that St. Pius V or St. Pius X had been time-warped forward in time to today and were shown the Conciliar Church in all its "glory". Would they recognize it as the Catholic Church, the One True Church founded by Our Lord Jesus Christ? Most certainly not.
Vatican I taught about supernatural faith that it depends upon a submission to authority. BUT the initial determination of the credibility of that authority does from from the use of reason, moved by grace. It's based on these motives of credibility that people determine, "Yes, this is the Church founded by Christ and it does have His authority."
Traditional Catholics have come to the realization that Bergoglio (and his predecessors) do not speak with the voice of the Shepherd. Our Lord taught that His sheep know His voice and obey it. We do not recognize the voice of Our Lord in the Conciliar Church. Our Lord also taught that we would know things by their fruits, and one could write many volumes about the fruits of the Conciliar Church.
We're not talking about an individual proposition in the docuмents of Vatican II. We're talking about an entirely new religion that was created that bears little resemblance (except in a few residual trappings) to the Catholic Church of Tradition.
What we see in Vatican II isn't just a handful of problematic statements (the 5% of Bishop Fellay), but we see an entirely new Modernist and subjectivist theological system that has manifested itself in 60+ years of "Magisterium". Vatican II cannot simply be "corrected," as per +Schneider, by simply amending one or two sentences. But it's radically defective throughout.
At the core of the Vatican II errors rests the Modernist-reimagined ecclesiology, an anti-Tridentine ecclesiology, where there's a "Church of Christ" that reaches beyond the Catholic Church. While the Catholic Church remains its "subsistent core," various schismatic sects are referred to as Churches. So then Vatican II details varying degrees of separation from this subsistent core, this "fullness of truth".
Thus, V2 concludes the equivalent of, Orthodox are 99% Catholic, Protestants (depending on the sect) can be 75%-90% Catholic, and even Jews and Muslims are at least, say, 25% Catholic. While I'm throwing arbitrary numbers out here, this illustrates the V2 approach to ecclesiology. Ironically, this is the same mentality +Fellay adopts when speaking of V2 being 95% Catholic.
This is a shift from the prior 1900+ years of Catholic theology, where you were either 100% Catholic or you were non-Catholic, a binary or discrete view, vs. this notion of a continuum of truth promoted by V2. Why? That's because supernatural motive of faith depends upon submitting in principle to the authority of Christ's Church. And that is why it's said that if you deny one dogma, you deny them all, because you're denying the very authority behind ALL dogmas. So even though certain "Churches" may MATERIALLY overlap with a significant percentage of Catholic dogmas, they're still radically separated from the Church based on this criterion. This is the Traditional teaching that's now replaced by Vatican II.
How does V2 do this? Well, it's rooted in subjectivizing the formal motive of faith, and transmuting it from a disposition of the intellect and the will to accept the Church's teaching into some strange form of "sincerity", where if you really believe that you're right, then you have the formal motive of faith and are only in material error with regard to whatever errors you hold. So the supernatural motive of faith, which used to be, "I recognize that the Catholic Church teaches with the authority of Christ and therefore accept everything it teaches," into "I want to believe what God wants me to believe." Supernatural Faith now depends not on some objective disposition of the intellect and will, but rather on some subjectivist "sincerity" and "intention". This is also the root of Religious Liberty. If I can have faith and please God by sincerely following my (even materially erroneous) beliefs, then, since I have a right to please God, then I have a right to follow my (even materially erroneous) beliefs.
This is the crux of the V2 problem, and the root of the entire V2 theological framework. And THIS is why the so-called "Feeneyism" question is so important. Rejection of Vatican II as non-Catholic is inseparable from the same problems that Father Feeney et al. are addressing.
Soteriology and ecclesiology are inextricably joined. We know as dogma that there's no salvation outside the Church. So if we want Orthodox and Prots and Jews and Muslims to be saved, we have to find a way to include them IN the Church. There's no other way to do that than by redefining Church.
MAJOR: There's no salvation outside the Church (dogma).
MINOR: Orthodox, Prots, Muslims, Jews can be saved.
CONCLUSION: Orthodox, Prots, Muslims, Jews can be IN the Church.
So you have to redefine "Church," which is precisely what Vatican II did.
Karl Rahner realized that this was THE fundamental shift at Vatican II (of course he was delighted with it), and he marveled that more of the conservative V2 Fathers didn't so much as make a peep about it. That's because this erosion of EENS and therefore of ecclesiology had been under way for a couple hundred years at least, and so it was already well entrenched. Vatican II didn't just come out of nowhere.
So this is the new theological system upon which the Conciliar Church has been established. We're not talking about one or two problematic statements, but upon a new ecclesiology and new soteriology, a new subjectivist theological system.
So, on top of that, we see a New Mass that's not a lick different from Cranmer's abomination and different very little from Luther's. Some of the English martyrs proclaimed that they would give their lives for the slightest ceremony in the Catholic Mass. Conciliar Church spits on their graves and adopts the liturgical theology of the heretical Protestants.
In addition, we have the myriad bogus canonizations (for political reasons) by the Conciliar Church ... applying the criterion of "sincerity", or "nitheness", as Bishop Williamson famously refers to it, rather than objective heroic virtue.
With the new theological system (radically different and not just consisting of a couple propositions), a new Protestantized form of Public Worship (Mass), and a new cult of the saints ... the Conciliar Church is in fact an entirely brand new religion that breaks continuity with the Traditional Catholic Church.
So THIS is how Traditional Catholics have come to a recognition that the Conciliar Church is not the Catholic Church, as their sensus Catholicus has determined that there is a substantial discontinuity and disconnect from the Catholic Church prior to Vatican II, and not based on some modo tollentis argument regarding this, that, or another Vatican II proposition. We find that this Conciliar Church lacks the motives of credibility, that it lacks the Notes of the One True Church of Christ, and is therefore not recognizable as such. St. Pius V and St. Pius X would not recognize it as such ... and neither do we.