They didn't want to "leave the Church," you're right. Instead, they wanted to make the entire Church over into what THEY felt was the Truth.
Eric, I don't know how to make you see that you're just continuing to beg the question here. A neo-Catholic could easily turn that argument right back around at you and say that's exactly what Traditionalists are doing. You (y'all) don't agree that the Church of Christ subsists in the Catholic Church; you don't agree that Protestants and Eastern Orthodox are in "partial communion" with the Church; you don't agree that the Mass should have been reformed; you don't agree that Muslims worship the one God who made heaven and earth; and on and on it goes.
So although the Church has taught these things as part of the ongoing clarification of what is contained in the deposit of faith, you see in it a contradiction and a rejection of Tradition; therefore, you want to "make the entire Church over into" what you think is the Truth.
However, their ideas of truth were their own, pure and simple, or perhaps regurgitations of some past heresy. OUR ideas of Truth, on the other hand, are the truths which have been handed down through 20 centuries of Supreme Pontiffs speaking Ex Cathedra, Dogmatic Ecumenical Councils, and the like.
Again, begging the question. Do you think the heretics of the 16th century didn't claim exactly the same thing? You should read John Calvin's Institutes of Christian Religion sometime; he quotes Father after Father to show how the Roman Church had contradicted in his own "modern" time the "truths which have been handed down."
The point of what I'm getting at is this: our first clue, as Catholics, as to whether or not something really belongs to the authentic deposit of faith, as part of our Tradition, is that the Church teaches it. We acknowledge Her as the guardian of Tradition, the only authority on earth who can say "this is in line with Tradition," or "this is not in line with Tradition."
Now then, if we deny Her that authority in the years 1962-1965, then we implicitly seem to be saying that She is not, in fact, the sole guardian of Tradition and teacher of the Deposit of Faith; we might admit that She usually is such, but not always, and therefore not "solely." Apparently that honor belongs to someone or something else. I'm asking who that authority is? Is it me, myself, and I? The Church suggests what is Traditional, and I render the final decision? Is it Bishop Fellay? You seemed to be suggesting earlier that this role of "guardian" has passed - nay, has been postively given by God - to the SSPX.
I'm trying the untangle the epistemological knot that this ties.
How do you square the entire tradition of the Church, the condemnations of "Bible societies" under Gregory XVI and Pius IX, the Syllabus, the condemnation of the Sillon under Pius X, Pius XI's Mortalium Animos, etc. with the pure ecumenist novelty coming from the Vatican today? You cannot. We hold to Eternal Rome, not Rome when it gives us the neo-Protestant tendencies, as the Archbishop said.
More begging of the question. The matter still lies open: who is the final arbiter of the truth here? Who is the final guardian of Tradition? Who has the authority to clarify the contents of Sacred Tradition, to tell us what is truly eternal in it (and therefore "Tradition" with a capital "T"), and what was merely custom or passing opinion (and therefore "tradition" with a small "t")?
In short, who gets to decide when "Rome" and "Eternal Rome" are one and the same thing, and when they have parted ways? Is that up to my powers of observation? Does that charism belong to Archbishop Lefebvre? To the SSPX as a whole? To anyone at all? Is such a distinction between "Rome" and "Eternal Rome" anywhere taught in the saints, doctors, councils, or popes of the past? Or is this a modern novelty and innovation, and therefore itself a departure from Tradition?
I see a great irony in the fact that we don't mind dissecting Vatican II and declaring some of it to be non-binding, but then when a Modernist does the exact same thing with Trent or Vatican I, we go nuts. We don't seem to have a problem cutting up Benedict XVI's encyclical, or JP2's encyclicals, but when a Modernist does the exact same thing with non-infallible encyclicals of Leo XIII (on Church and State), Pius IX (on modern errors), or Pius XI (on the kingship of Christ in society), we insist that these are papal teachings and must be accepted.
If you tell me I can reject Vatican II's teaching on ecumenism, even though it's an Ecumenical Council teaching with the power of the Supreme Ordinary Magisterium, then you can't tell me not to reject Pius XI's encyclical on ecumenism either.
The point is, this is not the way Catholics of the past used to think; and since we're trying to emulate the Catholics of the past, then why aren't we adopting their stance towards Rome (and don't say "because Rome has departed from Tradition," because no Catholic of past ages would have ever let you get away with saying something so preposterous)?
By the way, let me make this clear: I'm playing Devil's Advocate here because these are serious questions, and they need to be asked. We really are talking about the difference between being in the Church or outside the Church - schism is a matter of the heart long before it becomes an official decree, so just because the pope hasn't declared me to be in schism doesn't mean I'm not. And if we take seriously the position of EENS, then these are not abstract questions - and you'll forgive me if I find that the "pat answers" are just not doing justice to the issues.
To HMiS: back off, man. I haven't judged anyone, collectively or personally. I'm asking a legitimate question. If it would help to keep people's egos from getting bruised, I can stick to the first-person-singular from now on.