This is actually not true.  But even if it were, why should we believe the same people who gave us Vatican II in the first place?

Pope Paul VI made it clear in a public audience of January 12th, 1966 that the decrees of Vatican II were never stamped with the note of infallibility as he openly declared:

“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)

Not infallible in an extraordinary,solemn manner, but according to the Supreme Ordinary Magisterium:

There are those who ask what is the authority, the theological qualification, that the Council wished to attribute to its teachings, knowing that it has avoided giving solemn dogmatic definitions, committing the infallibility of the ecclesiastical magisterium. And the answer is known to those who remember the conciliar declaration of March 6, 1964, repeated on November 16, 1964: given the pastoral character of the Council, it avoided pronouncing in an extraordinary way dogmas endowed with the note of infallibility; but it has nevertheless endowed its teachings with the authority of the supreme ordinary magisterium which ordinary and so clearly authentic magisterium must be accepted docilely and sincerely by all the faithful, according to the mind of the Council regarding the nature and purposes of the individual docuмents. - Paul VI, General Audience, January 12, 1966.

but it has nevertheless endowed its teachings with the authority of the supreme ordinary magisterium which ordinary and so clearly authentic magisterium must be accepted docilely and sincerely by all the faithful, according to the mind of the Council regarding the nature and purposes of the individual docuмents. - Paul VI, General Audience, January 12, 1966.

Yep...just check out the smart aleck response from SJ. They're objective schismatics.

Oh?

My comment may contain irony, since it turned your rebuttal against you, but it is also perfectly accurate: No Pope can claim infallible status through the ordinary magisterium for a novelty:

“Thus the truth that is taught must be proposed as already defined, or as what has always been believed or accepted in the Church, or attested by the unanimous and constant agreement of theologians as being a Catholic truth [which is therefore] strictly obligatory for all the faithful." ("Infaillibilite du Pape", DTC, vol. VII, col. 1705)”

https://sspx.org/en/clear-ideas-popes-infallible-magisterium

Obviously, teachings which fail this test can hardly lay claim to infallibility

PS: The article containing the quote is outstanding.

Pope Francis: There are many ‘restorers’ in the US who do not accept Vatican II

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Pope Francis sat at the front of the congregation in St. Peter's Basilica on the Solemnity of Pentecost on June 5, 2022. | Vatican Media

By Hannah Brockhaus
Vatican City, Jun 14, 2022 / 04:12 am
There are many “restorers” in the United States who do not accept the Second Vatican Council, Pope Francis said in an interview published on Tuesday.
Speaking to the editors of Jesuit journals, he criticized what he called “restorationism” in the Church, which he defined as the failure to accept Vatican II, the ecuмenical council held from 1962 to 1965.
He said: “Restorationism has come to gag the Council. The number of groups of ‘restorers’ — for example, in the United States there are many — is significant.”
“An Argentine bishop told me that he had been asked to administer a diocese that had fallen into the hands of these ‘restorers.’ They had never accepted the Council. There are ideas, behaviors that arise from a restorationism that basically did not accept the Council.”
“The problem is precisely this: in some contexts, the Council has not yet been accepted. It is also true that it takes a century for a Council to take root. We still have 40 years to make it take root, then!”
Pope Francis cited opposition to Vatican IIwhen he issued the motu proprio Traditionis custodes in July 2021, limiting celebrations of the Traditional Latin Mass.
In a letter to the world’s bishops, he said he was saddened that the celebration of the Traditional Latin Mass was “often characterized by a rejection not only of the liturgical reform, but of the Vatican Council II itself.”
To doubt the Council, he said, is “in the final analysis, to doubt the Holy Spirit himself who guides the Church.”
The pope’s conversation with editors, which also touched on the war in Ukraine and the German “Synodal Way,” was published in La Civiltà Cattolica on June 14 but was conducted on May 19.

[T]here are those who, under the pretext of a greater fidelity to the Church and the Magisterium, systematically refuse the teaching of the Council itself, its application and the reforms that stem from it, its gradual application by the Apostolic See and the Episcopal Conferences, under our authority, willed by Christ. Discredit is cast upon the authority of the Church in the name of a Tradition, to which respect is professed only materially and verbally. The faithful are drawn away from the bonds of obedience to the See of Peter and to their rightful Bishops; today’s authority is rejected in the name of yesterday’s. And the fact is all the more serious in that the opposition of which we are speaking is not only encouraged by some priests, but is led by a Prelate, Archbishop Marcel Lefebvre, who nevertheless still has our respect.

It is so painful to take note of this; but how can we not see in such an attitude—whatever may be these people’s intentions—the placing of themselves outside obedience and communion with the Successor of Peter and therefore outside the Church? 

For this, unfortunately, is the logical consequence, when, that is, it is held as preferable to disobey with the pretext of preserving one’s faith intact, and of working in one’s way for the preservation of the Catholic Church, while at the same time refusing to give her effective obedience. And this is said openly! It is even affirmed that the Second Vatican Council is not binding; that the faith would also be in danger because of the reforms and post-conciliar directives, that one has the duty to disobey in order to preserve certain traditions. What traditions? Is it for this group [=Lefebvrists], not the Pope, not the College of Bishops, not the Ecuмenical Council, to decide which among the innumerable traditions must be considered as the norm of faith? As you see, Venerable Brothers, such an attitude sets itself up as a judge of that divine will which placed Peter and his lawful Successors at the head of the Church to confirm the brethren in the faith, and to feed the universal flock (cf. Lk 22:32; Jn 21:15 ff.), and which established him as the guarantor and custodian of the deposit of faith.

And this is all the more serious, in particular, when division is introduced precisely where congregavit nos in unum Christi amor [the love of Christ has gathered us into one], in the Liturgy and the Eucharistic Sacrifice, by the refusing of obedience to the norms laid down in the liturgical sphere. It is in the name of Tradition that we ask all our sons and daughters, all the Catholic communities, to celebrate with dignity and fervor the renewed liturgy. The adoption of the new Ordo Missae [order of the Mass] is certainly not left to the free choice of priests or faithful. The instruction of 14 June 1971 has provided for, with the authorization of the Ordinary, the celebration of the Mass in the old form only by aged and infirm priests, who offer the divine Sacrifice sine popolo [without people attending]. The new Ordo was promulgated to take the place of the old, after mature deliberation, following upon the requests of the Second Vatican Council. In no different way did our holy Predecessor Pius V make obligatory the Missal reformed under his authority, following the Council of Tent.

With the same supreme authority that comes from Christ Jesus, we call for the same obedience to all the other liturgical, disciplinary and pastoral reforms which have matured in these years in the implementation of the Council decrees. Any initiative which tries to obstruct them cannot claim the prerogative of rendering a service to the Church; in fact it causes the Church serious damage.

Various times, directly and through our collaborators and other friendly persons, we have called the attention of Archbishop Lefebvre to the seriousness of his behaviour, the irregularity of his principal present initiatives, the inconsistency and often falsity of the doctrinal positions on which he bases this behaviour and these initiatives, and the damage that accrues to the entire Church because of them.

It is with profound sadness but with paternal hope that we once more turn to this confrère of ours, to his collaborators and to those who have let themselves be carried away by them. Oh, certainly, we believe that many of these faithful—at least in the beginning—were in good faith: we also understand their sentimental attachment to habitual forms of worship or of discipline that for a long time had been for them a spiritual support and in which they had found spiritual sustenance. But we are confident that they will reflect with serenity, without closed minds, and they will admit that they can find today the support and sustenance that they are seeking in the renewed forms that the Second Vatican Ecuмenical Council and we ourself have decreed as being necessary for the good of the Church, her progress in the modern world, and her unity. We therefore exhort yet once again all these brethren and sons and daughters of ours; we beseech them to become aware of the profound wounds that they otherwise cause to the Church, and we invite them again to reflect on Christ’s serious warnings about the unity of the Church (cf. Jn 17:21 ff) and on the obedience that is due to the lawful Pastor placed by him over the universal flock, as a sign of the obedience due to the Father and to the Son (cf. Lk 10:16). We await them with an open heart, with arms ready to embrace them; may they know how to rediscover in humility and edification, to the joy of the whole People of God, the way of unity and of love! - Paul VI, Allocution to the Consistory, May 24, 1976