As I understand it, the changes in the liturgy after Vatican II were a big part of the rationale, but the key issue was the declaration on religious liberty. Unless I’m mistaken, the SSPX believe that was a flat-out error in doctrine, which, they say, is evidence that the Council was illegitimate and its declarations not binding.
They were excommunicated when the founder, Archbishop Lefebvre, performed episcopal ordinations without authorization. There’s a legitimate apostolic succession, which is why their ordinations are valid and the Eucharist is the true Sacrament, but their whole organization is contrary to canon law (as understood by those who say such things, such as Pope Benedict).
Every so many years I have to re-read a summary of Dignitatis Humanae, and how it does or doesn't differ from earlier ideas about religious freedom from the time of Christendom (original meaning), but even then end up with a fairly hazy feeling about the whole thing.
At any rate, the expressed preference in Vatican II for Democratic Liberalism, knowing those two words are not used exactly as they typically would be on this forum, but kinda/sorta are, continues to make me uncomfortable.