The labels which Vatican II gives to its documents do not show that any of them teach infallibly. These labels merely show the council’s intellectual sloppiness.
There are many superficial reasons for supposing that Vatican II infallibly teaches truth and does not teach error. However, those suppositions are false. There are many proofs that Vatican II’s teachings are not infallible. For example:
Read the full explanations of these proofs that Vatican II is not infallible, in this article: ../faith/vatican-ii-is-not-infallible.html

Examination of another argument, viz., that certain documents of Vatican II are infallible based on their being designated as “dogmatic constitutions”.

There is another superficial argument sometimes given for supposing that Vatican II’s teachings are infallible (however much they plainly seem to contradict the truth).
According to this argument, Vatican II must teach infallibly at least in those documents which are called “dogmatic constitutions”, e.g., the council documents called Lumen Gentium and Dei Verbum. This argument supposes that those documents are infallible because Catholic dogma is infallible and the council’s label shows (supposedly) that those documents teach dogma.
But this supposition contains an unsupported assumption. Vatican II labeled these documents “dogmatic constitutions” but that label does not tell us that these documents infallibly define dogma. Those documents could be labeled “dogmatic constitutions” because they discuss dogmatic subjects without themselves infallibly defining any dogma.
On the other hand, other Vatican II documents which are not called “dogmatic constitutions” also discuss dogmas (and teach heresies against dogmas). Why aren’t those other documents also called “dogmatic constitutions”? What does that label tell us, if anything?
A prominent Protestant observer at Vatican II, Dr. Robert McAfee Brown, gave his eye-witness impression regarding the labels which the council placed on its documents:
In those early days of the Council there was much discussion about the relative degree of binding authority between, say, a ‘constitution’ and a ‘decree.’ It seemed fairly clear that a ‘constitution’ was of higher authority, and it would be a wise rule of interpretation to say that the ‘constitution’ On the Church [i.e., Lumen Gentium], for example, was the context in which to understand the ‘decree’ On Ecumenism, rather than vice versa. As it actually worked out, however, there seemed little reason by the end of the Council why The Church in the World Today [i.e., Gaudium et Spes] should be a ‘constitution’ (albeit a ‘pastoral constitution’) while the document on Missionary Activity should be a ‘decree’ or the statement on Religious Freedom a ‘declaration’.1
Our own research supports McAfee Brown on this historical point, viz., that there was not, and still is not, any authoritative clarity or any consistent and comprehensive rationale regarding the respective weights of the documents, based on their designated labels (viz., “dogmatic constitution”, “pastoral constitution”, “decree” or “declaration”). This lack of clarity is exemplified in Pope Paul VI calling the Declaration on Religious Liberty “one of the greatest documents of the Council”2 even though it has what seems to be the lower status of a “declaration”.
This uncertainty fits with the revolutionary character of the council (and of the conciliar church since then), viz., that just like in other revolutions, much that occurs is unclear and in flux.3
All Vatican II documents are evil.4 But regardless of whatever authority the council might be supposed to give the documents, there is no reason to suppose that their labels designate any of them as teaching infallibly, i.e., by the fact that the council teaches in a document designated as a “dogmatic constitution”.

Nothing in the conciliar church is carefully done or well thought-out.

The fruits of the conciliar church are not only evil, but are shallow. For example, the new mass is not only a sacrilege, but its inner emptiness is obvious from its banal outward manifestations, for example:
The conciliar church is empty of meaning and is being emptied of people.

Protestant and conciliar intellectual bankruptcy

The conciliar church is merely “warmed over” Protestantism. As a consequence, it has no serious intellectual content (as the Protestants have none either). Before Vatican II, any large Catholic bookstore was replete with the riches and wisdom of 2000 years of the Church, e.g., St. Thomas Aquinas, the Imitation of Christ, St. Bernard of Clairvaux, St. Augustine, Gregorian Chant, and so many other works from many centuries ago.
By contrast, walk into a Protestant bookstore before or after Vatican II, and you would find it is full of “bestsellers” and new, short-lived titles, because Protestantism has no serious legacy to offer from its five centuries of revolutionary existence.
The conciliar church is like Protestantism. Conciliar bookstores are full of new (post-Vatican II) offerings which are quickly replaced by the next fad-of-the-day and are forgotten. The conciliar church has no deep and penetrating theology or philosophy. Nothing conciliar is carefully done or well thought-out.
Under the guidance of the Holy Ghost, the Catholic Church has comprehensively worked out true theology and philosophy. In comparison, Protestant and conciliar thinkers are “lightweights” and amateurs (as well as revolutionaries). The edifice of Catholic intellectual patrimony, compared to Protestant and conciliar thought, is like a magnificent cathedral compared to a few sticks leaning against each other.
The haphazard way in which the documents of Vatican II were labeled, is an example of intellectual sloppiness and was a harbinger of what would come (and now exists) in the post-conciliar church.

Conclusion

The conciliar church does not have the answers any more than Protestantism does. They have nothing to add or give us except harm and evil.6 Let us be ever grateful for the great spiritual and intellectual treasures of Catholic Tradition and enrich ourselves with them every day through study and prayer!
Catholic Candle note:
The conciliar church is Catholic in name only. A Catholic will gradually lose his Faith if he fails to understand that. When he hears the word “Catholic” outside of the context of genuine Traditional Catholicism, he should guard himself against conciliar poison by understanding that this word refers to anti-Catholicism.
Archbishop Lefebvre declared the conciliar church is a different, false church.7 The “old” SSPX faithfully taught the same truth.8 The “new” SSPX rejects its founder’s position and denies that the conciliar church is a separate (and false) church.9 The N-SSPX priests and laymen will gradually lose their Faith under that delusion.
  1. Robert McAfee Brown, Ecumenical Revolution, Doubleday, Garden City, 1967 (2nd ed., 1969), p.176 (emphasis in original; bracketed words added for clarity).
  2. For an explanation why revolution is always wrong, read this article: ../faith/against-sedevacantism.html#section-6
  3. E.g., regarding the hundreds of errors in Vatican II’s document, Lumen Gentium, as they are compared to the consistent teaching of the Fathers, Doctors and popes throughout the ages, read this article: https://drive.google.com/file/d/0B49oPuI54eEGbzRhdmQ3X0Z6RFE/view
    There are about 19 errors per page in Vatican II’s document, Lumen Gentium. Read this explanation here: ../priests/sspx-the-new-sspx-claims-archbishop-lefebvre-endorsed-vatican-iis-lumen-gentium,-as-free-of-all-errors-and-ambiguities.html#fn17
    See also, e.g., regarding how Vatican II’s Dignitatis Humanae, teaches religious liberty for error and contradicts what the Catholic Church has always infallibly taught, read this article: ../faith/religious-liberty-vatican-ii.html
  4. For example, Cheerios and Chex were brought up as “gifts” during the new mass for the so-called “beatification” of Fr. Solano Casey. Watch at minute marker 1:53:40, at this link: https://video.search.yahoo.com/search/video;_ylt=AwrBT74Jhx1aax4A8A1XNyoA;_ylu=X3oDMTEyZWVzMmpzBGNvbG8DYmYxBHBvcwMzBHZ0aWQDQjQ0ODNfMQRzZWMDc2M-
  5. The conciliar church has nothing good in it. Read the explanation of this fact here: ../faith/nothing-good-conciliar-church.html
    The conciliar church’s new mass never gives grace. Read the explanation of this fact here: ../faith/new-mass-never-grace.html
  6. To read Archbishop Lefebvre’s declarations that the conciliar church is a different, false church, and for a more complete explanation of this fact, read these articles:
  7. Here are the words of the “old” SSPX (cited back to its own sources), that the conciliar church is a different and false church: ../priests/sspx-faithful-and-informed-catholics-reject-even-the-concept-of-recognition-by-modernist-rome.html
  8. Read the “new” SSPX’s own words (cited back to its own sources) in this article: ../faith/archbishop-lefebvre-the-conciliar-church-is-not-the-catholic-church-nor-a-mere-mindset-but-is-a-new-church.html