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Here is a link to a thorough refutation of the notion that Vatican II was not binding: Vatican II and its Authority
Here is an excerpt:

A truth is always taught infallibly by the ordinary magisterium before it is ever set forth in more solemn forms of exposition (if it ever is). However, this does not mean that a teaching of the ordinary magisterium is necessarily taught explicitly in words; it may be expressed by a doctrine implicitly contained in a Church practice which thereby receives the universal consent to qualify as definitive. What cannot be overlooked in this is that the Pope and the college of bishops at the Second Vatican Council gave a comprehensive presentation of the Catholic faith demonstrating in the process the doctrinal and moral unanimity of the united episcopate. This is sufficient to fulfill the criteria for an exercise of the ordinary and universal magisterium in matters that directly involve the teaching of doctrine. Indeed properly understood, the charism of infallibility is present whenever the episcopate in union with the Roman Pontiff teaches in concurrence on a point of doctrine whether they proclaim it by a recognizably definitive act or not. The Catholic Encyclopedia emphasizes this point in its article on General Councils:
All the arguments which go to prove the infallibility of the Church apply with their fullest force to the infallible authority of general councils in union with the pope. For conciliary decisions are the ripe fruit of the total life-energy of the teaching Church actuated and directed by the Holy Ghost. Such was the mind of the Apostles when, at the Council of Jerusalem (Acts, xv, 28), they put the seal of supreme authority on their decisions in attributing them to the joint action of the Spirit of God and of themselves: Visum est Spiritui sancto et nobis (It hath seemed good to the Holy Ghost and to us). This formula and the dogma it enshrines stand out brightly in the deposit of faith and have been carefully guarded throughout the many storms raised in councils by the play of the human element. From the earliest times they who rejected the decisions of councils were themselves rejected by the Church... The infallibility of the council is intrinsic, i.e. springs from its nature. Christ promised to be in the midst of two or three of His disciples gathered together in His name; now an Ecumenical council is, in fact or in law, a gathering of all Christ's co-workers for the salvation of man through true faith and holy conduct; He is therefore in their midst, fulfilling His promises and leading them into the truth for which they are striving. His presence, by cementing the unity of the assembly into one body -- His own mystical body -- gives it the necessary completeness, and makes up for any defect possibly arising from the physical absence of a certain number of bishops. The same presence strengthens the action of the pope, so that, as mouthpiece of the council, he can say in truth, "it has seemed good to the Holy Ghost and to us", and consequently can, and does, put the seal of infallibility on the conciliar decree irrespective of his own personal infallibility.
A General Council in short by its very nature is protected from error in doctrinal matters. What this means is that any dogma or doctrine proclaimed by the Pope and the Bishops in union with him is properly understood as being set forth infallibly. To doubt this is to doubt the validity of the other twenty ecumenical councils of the Catholic Church. Also, even decisions not infallibly declared are still to be given a religious submission of mind and will (Matt. 10:40, Luke 10:16, John 13:20; Canon 752). Catholics who refuse to do these things are not Catholics at all but instead are schismatics.

Neither you--nor this unnamed site you indicate as a source--seem to be able to reason clearly. I say this because it was THE POPE HIMSELF, Paul VI, who ordered that his notice be read to the Council Fathers, prohibiting them from promulgating anything binding on the Church without prior notice. As it turned out, no such prior notice was ever given about anything. Therefore nothing was ever declared infallible. What part of this can't you understand? Here is what the Nota Praeva said once again:

"Taking conciliar custom into consideration and also the PASTORAL PURPOSE of the present Council, the sacred Council defines as binding on the Church only those things in matters of faith and morals which it SHALL OPENLY DECLARE TO BE BINDING. The rest of the things which the sacred Council sets forth, inasmuch as they are the teaching of the Church's supreme magisterium, ought to be accepted and embraced by each and every one of Christ's faithful according to the mind of the sacred Council. The mind of the Council becomes known either from the matter treated or from its manner of speaking, in accordance with the norms of theological interpretation."

Once again, nothing was openly declared binding by the Council. Therefore nothing was ever binding. Any talk of infallibility is consequently nonsense. But you can keep posting these non-sequiturs, if you wish--though they have no authority whatsoever except to present the opinions of those who oppose Catholic Tradition and who want everybody else to click heels and follow behind. We've seen where they've been leading the Church for forty years--over the cliff to disaster. No thanks.

Vatican II was unique in a number of ways from all other councils. None other was self-described as pastoral nor proscribed by the pope for this reason from declaring that anything was binding. Vatican II was also unique in the descriptive and metaphoric language it used, deliberately designed to inspire rather than to instruct. For this reason much of what it declared was ambiguous and subject to extremely diverse interpretations. Of their very nature, moreover, such declarations cannot bind intellectually. Only clearly presented doctrines can do that.

To say this is clearly threatening to some, which is why they frequently use invective, rather than reason, to argue their points. These are the same people who have constructed their vision of a renewed Church on the chimera of some "Vatican II Spirit"--which is turning out to be not so much a renewal as a calamity. So is talk of anything having been taught infallibly by the Council, or talk about a "New Advent" or a "New Pentacost." For true Catholics, the old Pentacost was sufficient; so was the first and only Advent. Anything over and beyond the traditional faith, expressed in such bogus terms, is obviously suspicious and probably should be rejected.