I tire of arguing with this fraction of a percentage of the "Catholic" world. Yet, arguments are brought forth, and for whatever reason, I feel obligated to address them.
So a question arises: What could be so bad as to deem Pope Paul VI and every pope ever since to not be popes?
Sede answer: Pope Paul VI was a heretic.
New question: What made him a heretic?
Sede answer: His promulgation of Vatican II.
In the online Traditionalist community, I've tried boiling it down to specifics. Thus far, there are two specific things that irk the schismatic sedevacantists who have broken from their obedience to the one and only Catholic Church:
-The new Catechism of the Catholic Church
-Lumen Genitum, a Vatican II document
Trouble is, neither is an infallible work. And even Pope Paul VI stated that the Second Vatican Council was not a Council of infallible teachings :
"There are those who ask what authority, what theological qualification, the Council intended to give to its teachings, knowing that it avoided issuing solemn dogmatic definitions backed by the Church's infallible teaching authority. The answer is known by those who remember the conciliar declaration of March 6, 1964, repeated on November 16, 1964. In view of the pastoral nature of the Council, it avoided proclaiming in an extraordinary manner any dogmas carrying the mark of infallibility."
Pope Paul VI, January 12, 1966
I have yet to hear of a pope teaching anything ex cathedra that is contrary to what Christ taught.