Clearly Vatican II is "defining" teaching about various subjects. Only note left to discern is whether or not it's BINDING. That would be necessary for strict infallibility. But being binding and "obligation" is not required for being protected by indefectibility.
You treat indefectibility as if it's a backup to infallibility, when infallibility is not being used. Which in effect, you are arguing that EVERY sentence at a council is protected from error. If you say i'm being extreme, then I'll ask, 'how do you know which sentences are 'protected from error' and which ones aren't'? No one can answer this. So your view is not based on facts but your own interpretation of what indefectibility means.What teaching is infallible?
A word or two under this head, summarizing what has been already explained in this and in other articles will suffice.
As regards matter, only doctrines of faith
, and facts so intimately connected with these as to require infallible determination, fall under the scope of infallible ecclesiastical
teaching. These doctrines or facts need not necessarily be revealed; it is enough if the revealed deposit cannot be adequately and effectively guarded and explained, unless they are infallibly determined.
As to the organ of authority by which such doctrines or facts are determined, three possible organs exist. One of these, the magisterium ordinarium
, is liable to be somewhat indefinite in its pronouncements and, as a consequence, practically ineffective as an organ. The other two, however, are adequately efficient organs, and when they definitively decide any question of faith
that may arise, no believer who pays due attention to Christ's
promises can consistently refuse to assent with absolute and irrevocable certainty
to their teaching.
But before being bound to give such an assent, the believer has a right
to be certain that the teaching in question is definitive (since only definitive teaching is infallible); and the means by which the definitive intention, whether of a council or of the pope
, may be recognized have been stated above. It need only be added here that not everything in a conciliar
pronouncement, in which some doctrine
is defined, is to be treated as definitive and infallible. For example, in the lengthy Bull
of Pius IX
defining the Immaculate Conception the strictly definitive and infallible portion is comprised in a sentence or two; and the same is true
in many cases in regard to conciliar
decisions. The merely argumentative and justificatory statements embodied in definitive judgments, however true
and authoritative they may be, are not covered by the guarantee of infallibility which attaches to the strictly definitive sentences — unless, indeed, their infallibility has been previously or subsequently established by an independent decision.http://www.newadvent.org/cathen/07790a.htm