The SSPX schism has been well documented. But the real issue is not their uncontested material schism, but their material heresy which they erroneously use to rationalize their schism. In theology, "material" simply means you did it. "Formal" means you deliberately willed it and therefore are culpable for doing it.
Everyone knows the Church has been in crisis for 50 years. But the SSPX and its supporters want the faithful to believe the crisis is so bad that a "state of necessity" has accrued, making it necessary to set aside major parts of canon law and operate as if Rome no longer calls the shots.
We're not talking about an individual act of disobedience on the part of the SSPX but a wholesale disregard for Rome's authority.
But what this alleged "state of necessity" entails is a situation where — the SSPX claims — truth and grace have failed universally in the Church from the Pope on down. The Society claims Vatican II is full of doctrinal errors, and these errors are being universally perpetuated from all the popes and the Magisterium since then till now.
The SSPX even claims the Novus Ordo Mass is intrinsically evil and no one should ever go to a Mass unless it's in the Old Latin Rite — and only then if it's offered by an SSPX priest. This recent video on the Society's website clearly states their long-held position in this regard.
It's necessary for them to view the Church crisis this way because only then do they feel justified in going rogue. But what they're describing is actually heretical as it denies the dogma of the indefectibility of the Catholic Church. Truth and grace cannot fail universally from the Pope on down. Christ said of Peter, "On this rock I will build my Church and the gates of Hell will not prevail against it."
In March 2009, Pope Benedict XVI wrote a letter explaining the SSPX separation is doctrinal in nature and not merely canonical or legal, as the SSPX would have the public believe.
The fact that the Society of Saint Pius X does not possess a canonical status in the Church is not, in the end, based on disciplinary but on doctrinal reasons. ... In order to make this clear once again: Until the doctrinal questions are clarified, the Society has no canonical status in the Church, and its ministers — even though they have been freed of the ecclesiastical penalty — do not legitimately exercise any ministry in the Church. ... In light of this situation, it is my intention henceforth to join the Pontifical Commission Ecclesia Dei — the body which has been competent since 1988 for those communities and persons who, coming from the Society of Saint Pius X or from similar groups, wish to return to full communion with the Pope — to the Congregation for the Doctrine of the Faith. This will make it clear that the problems now to be addressed are essentially doctrinal in nature and concern primarily the acceptance of the Second Vatican Council and the post-conciliar magisterium of the Popes. (emphasis added)
The Holy Father continues:
The Church's teaching authority cannot be frozen in the year 1962 — this must be quite clear to the Society. But some of those who put themselves forward as great defenders of the Council also need to be reminded that Vatican II embraces the entire doctrinal history of the Church. Anyone who wishes to be obedient to the Council has to accept the Faith professed over the centuries, and cannot sever the roots from which the tree draws its life.
Notice, too, how the Pope says the Pontifical Commission Ecclesia Dei was established "for those communities and persons who, coming from the Society of Saint Pius X or from similar groups, wish to return to full communion with the Pope."
He says communion with the Pope specifically and not communion generally with the Church for two reasons. First, as canon 751 reads, "Schism is the withdrawal of submission to the Supreme Pontiff or from communion with the members of the Church subject to him." Second, as St. Ambrose, Father and Doctor of the Church, said in the fourth century, "Where there is Peter, there is the Church."
To Peter was given the charismatic grace of infallibility. Only bishops united to Peter make up the authentic Magisterium. Only when the college of bishops is in union with its head is it a living and authoritative body. In like manner, faithful Catholics make up the sensus fidelium only when they are united with the authentic Magisterium, as Pope Benedict XVI taught.
Herein lies the point of doctrinal strife. The SSPX on its website FAQ questions many doctrinal points of Vatican II, many teachings of all the popes since then, and even the Catechism of the Catholic Church. The Society and its sympathizers have placed themselves above the Magisterium and the popes as the supreme judge in matters of faith and morals.
As Pope Benedict said above, "The Church's teaching authority cannot be frozen in the year 1962." The SSPX, following the path of Martin Luther, has made an art of privately interpreting magisterial statements out of context, and pitting them against conciliar and post-conciliar statements in complete disregard of the authentic Magisterium. The Society's FAQ on Vatican II, the popes, and the Catechism all give ample evidence of this.
And it's because the SSPX has done this that Pope Benedict XVI turned the Society over to the Congregation for the Doctrine of the Faith, in order to "make it clear that the problems now to be addressed are essentially doctrinal in nature and concern primarily the acceptance of the Second Vatican Council and the post-conciliar magisterium of the Popes."
One SSPX priest vividly describes the real dangers of not reconciling with Rome, wherein he laments:
We have been living in independence from the Pope and the bishops for a very long time, as if that were normal. We pretend to defend the doctrine, but we all run the risk of establishing a chosen doctrine, abandoning certain dogmas, those that bother us, especially those concerning the primacy of Peter. ... Rome is no more than a pilgrimage site, and the Church is a Mystical Body with Jesus Christ for a head, the Holy Ghost for a soul, and the "Trads" for members. Our priests can quickly become gurus. Everyone could be a Pope with his Denzinger in hand, and every father of every family could be the Pope of his family. As for authority ... recognized in principle but not admitted in fact as far as the Pope is concerned, it risks no longer being recognized at any degree whatsoever. ... [Even] families will fall apart. Why obey a father who does not obey the Pope, the bishop, the priest?
May we all pray for the SSPX to be reunited with Rome not only for its sake but for ours as well, as we unite to battle what Bp. Athanasius Schneider calls the "fourth great crisis of the Church."