892 Divine assistance is also given to the successors of the apostles, teaching in communion with the successor of Peter, and, in a particular way, to the bishop of Rome, pastor of the whole Church, when, without arriving at an infallible definition and without pronouncing in a “definitive manner,” they propose in the exercise of the ordinary Magisterium a teaching that leads to better understanding of Revelation in matters of faith and morals. To this ordinary teaching the faithful “are to adhere to it with religious assent” which, though distinct from the assent of faith, is nonetheless an extension of it.
—Catechism of the Catholic Church
I find that when encountering a member of the SSPX (Society of St. Pius X) or a sympathizer of the group, they try to portray themselves as reasonable Catholics. But when pressed on how Church teaching requires them to give obedience to the teachings of the current Pope and those in communion with him, it quickly disintegrates into a claim that faithful Catholics have the right to compare the teachings of the Church today with the older teachings of the Church. If they decide that the two are different, they claim the right to disobey the living magisterium in favor of past documents.
The problem with this argument is it assumes as true what needs to be proven—that their interpretation of the past Church documents is correct and the current Pope and bishops in communion with him are not. In other words, begging the question. The argument makes use of premises that assume the conclusion is true. The real irony here is that the SSPX, determined to save the Church from being “Protestantized” (a common allegation being that Vatican II introduced Protestant error into the Mass and Church teaching) is actually employing the same argument that Martin Luther did—that the Church had fallen into error because her understanding of Scripture did not match his understanding of Scripture. So if Martin Luther was wrong to put his interpretation above the authority of the Church (which the SSPX would argue), then it is also wrong for the SSPX to do so.
There’s another problem with the SSPX attack on the authority of the Church from Vatican II on. If the Church taught error in something that binds the faithful then we have a problem which far exceeds the question of the form of the Mass and how ecumenism is to be practiced. We have a very real problem that forces us to ask, “How then do we know that the Church did not fall into error in a previous Council or Papal teaching? Someone could ask whether Vatican I erred in defining Papal Infallibility or Nicea I in defending the Trinity against the Arians. Once you claim that an Ecumenical Council can teach error, you open the floodgates of relativism, where each person decides for himself or herself what is true and what is not in Catholic teaching.
Either we believe God protects His Church under the Pope from teaching error in all ages, or we cannot be certain He protected the Church at all. The Church herself has always taught that her formal teaching, where she intends to teach the faithful (which includes encyclicals and apostolic exhortations) is binding. We can’t set aside Vatican II any more than a modernist can set aside Humanae Vitae.
In addition, we have this problem: Isn’t it possible that the people who see contradiction between older Church documents and the current teaching have missed the point of the original teaching, the current teaching or even both? To claim that they have properly understood both and can see a contradiction again requires proof that they have interpreted both, otherwise it's begging the question again.
Ultimately, when I run into a supporter of the SSPX in a forum or on Facebook, I think the real issue is that they have lost faith in God protecting the Church because the Church did not interpret the past teachings the way they think it ought to have been interpreted. They have elevated their preferences to being infallible doctrines while the successors of those whom Christ gave authority over the Church are presumed to be heretical or incompetent. That’s a terribly blinding pride which keeps them from seeing what they are denying—the promise of Christ to be with His Church always and that the gates of hell would not prevail against it. That’s a promise He made to St. Peter, and we believe He has been faithful in keeping it with every one of his successors, including Pope Francis.
Think of that when encountering a supporter of the SSPX, or someone who justifies their disobedience to the Pope today in the name of what they think the Church was in the past. Think of that and pray for them.