This is the single teaching of the Church that entirely refutes all of the more serious accusations against Pope Francis: each Pope has the charism of truth and of never failing faith (Vatican I, Pastor Aeternus, ch.4, n. 7). The charism of truth prevents him from teaching heresy or any grave error, and the charism of never failing faith preserves him in true faith so that he can never commit the sins of apostasy, heresy, or schism, not even personally and privately. And these charisms are actually One Charism, one gift, which has those two effects.
Some theologians even after Vatican I continued to opine that Popes could teach or commit heresy. So? Some theologians even today put forth opinions contrary to the teachings of past Ecumenical Councils, even Florence or Trent. After the first Ecumenical Council condemned Arius, Arianism continued for over 50 years until the second Ecumenical Council against condemned it. What theologians opine comes to an end when an Ecumenical Council issues a definitive teaching.
Some claim that the charism of truth and never failing faith is just the ability to teach under Papal Infallibility. Well, that makes no sense at all. The PI dogma is stated later in the same document. That section on the Charism is an authoritative interpretation of Luke 22:32 and the never failing faith of Peter.
And the meaning of that text in Vatican I on the faith of Peter (and his successors) is made absolutely clear by a review of the past teachings of the Magisterium on the same topic here.
It means that the Pope cannot teach grave error (when exercising the Magisterium) and he cannot fail in faith gravely, by apostasy, heresy, or schism.
Any past examples where the Pope supposedly taught or committed heresy are less authoritative than the teaching of an EC, and so those examples cannot refute the Council’s teaching. For the examples are a violation of the teaching: The First See is judged by no one. So you have to violate that teaching, to even begin to make that argument, which is a matter of prudential judgment, if it were even permitted to judge a Pope. The argument from alleged examples fails.
And of course the implicit argument is that the papal accusers themselves cannot possibly teach or commit heresy because they are supported by other persons who are like-minded. The many grains of sand agree with one another, so they cry out against the one Rock, with accusation after accusation. Their assurance that they are right and the Pope is wrong is their number. But Christ did not found His Church on the many grains of sand, but on the one Rock.
I will always trust in the Roman Pontiff, who cannot teach or commit heresy, and who cannot err gravely in doctrine or discipline. You grains of sand will be swept away by the sea.