The SSPX and other traditionalists have problems with Vatican II mostly on account of the thought-form and world-feeling that emerge from the conciliar documents. Search as they might, they cannot find the religion that elevates their souls in the present manner of the Catholic Church. To their souls, the Church has become concrete, glass, and steel- whereas their spirits thirst not simply for incense climbing the Gothic vault but for sanctuaries where all ancient symbols go untouched by modern eyes, touch, and thoughts. The entire project of the Council cannot but appear a monstrosity to them. It is the difference between communion received kneeling and on the tongue versus communion received in the hands while standing. Their religion is poetry and the Council’s is prose. Some of them might piece together arguments after they have experienced the breech between what they feel to be transcendence and what they see in the contemporary Church. Ultimately, such things are rationalization, which is why they are so poorly argued. Besting them in debate is easy. Presenting them evidence of their disobedience is similarly not a challenge. They fly only all the more into a rage and insist upon the truth of their position, because their hearts cannot rest inside so cold and alien a space as the present world.
Only orders such as your own, Reverend Father, have any hope of drawing them back, specifically by its promotion not simply of devotion to Mary but of the kind of devotion to her that hearkens to the spirit of St. Bernard and all that entails.