If the universal teaching authority, i.e. the pope and the bishops with moral unanimity, pass on to the faithful a teaching as revealed, the faithful are obliged under pain of heresy to believe that doctrine with divine faith.
IIRC, during the Arian heresy, 90% of the teaching authority succumbed to error.
Moreover in the celebrated case of religious liberty, concerning which Vatican II flagrantly taught in almost identical words the direct opposite of Pope Pius IXsQuanta Cura (an act of the Extraordinary Magisterium), the Council insisted that its doctrine concerned a natural human right founded on the dignity of the human person as made known by divine revelation.
In this case, Divine Revelation was invoked to justify flaunting the teachings of the Extraordinary Magisterium? If this teaching is automatically infallible, then to be a believing Catholic is in essence to be at the mercy of capricious churchmen whose doctrines du jour MUST be accepted as infallible, even if they contradict previous infallible teachings, and without reference to the Deposit of Faith [the sum total of revealed truths given by Christ to his Church; truths guarded by the Church and taught infallibly (The Concise Catholic Dictionary, Imprimatur Archbishop of Milwaukee, 1943)]
Faith and reason must always be in harmony.
5. Even though faith is above reason, there can never be any real disagreement between faith and reason, since it is the same God who reveals the mysteries and infuses faith, and who has endowed the human mind with the light of reason. Vatican I
It is all we need to make good the claim that Vatican II fulfilled the conditions for infallibility if Paul VI was a true pope. For it was certainly an occasion on which, in all appearance, pope and bishops united in transmitting to the faithful a substantial body of religious tenets presented as being authentic Catholic doctrine.
Authentic Catholic doctrine must conform to the Deposit of Faith and to Magisterial teachings.
13. For the doctrine of the faith which God has revealed is put forward not as some philosophical discovery capable of being perfected by human intelligence, but as a divine deposit committed to the spouse of Christ to be faithfully protected and infallibly promulgated.
14. Hence, too, that meaning of the sacred dogmas is ever to be maintained which has once been declared by Holy mother Church, and there must never be any abandonment of this sense under the pretext or in the name of a more profound understanding. Vatican I