"
As far as I can tell, learned people don't express their opinions as either ""Vatican II is infallible"" or ""Vatican II is not infallible"".  Everyone is pretty much agreed that ecumenical councils exercise their infallibility via the promulgation of dogmatic definitions, so the question really is whether Vatican II promulgated any dogmatic definitions.  Even the famous Pope Paul VI quote that traditional Catholics always cite uses this terminology:
“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.” (General Audience, December 1, 1966, published in the L'Osservatore Romano 1/21/1966)
   "