The Pope can commit heresy personally. He just can’t define it ex cathedra as binding on the whole Church.
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Please consider this quote in rebuttal to your above claim:
The question was also raised by a Cardinal, “What is to be done with the Pope if he becomes a heretic?” It was answered that there has never been such a case; the Council of Bishops could depose him for heresy, for from the moment he becomes a heretic he is not the head or even a member of the Church. The Church would not be, for a moment, obliged to listen to him when he begins to teach a doctrine the Church knows to be a false doctrine, and he would cease to be Pope, being deposed by God Himself.
If the Pope, for instance, were to say that the belief in God is false, you would not be obliged to believe him, or if he were to deny the rest of the creed, “I believe in Christ,” etc. The supposition is injurious to the Holy Father in the very idea, but serves to show you the fullness with which the subject has been considered and the ample thought given to every possibility. If he denies any dogma of the Church held by every true believer, he is no more Pope than either you or I; and so in this respect the dogma of infallibility amounts to nothing as an article of temporal government or cover for heresy.
(Abp. John B. Purcell, quoted in Rev. James J. McGovern, Life and Life Work of Pope Leo XIII [Chicago, IL: Allied Printing, 1903], p. 241)
(From: http://novusordowatch.org/2015/04/vatican-i-popes-follow-up/)
I don’t see the contradiction with what I posted.
Honorius promoted/allowed a heresy, and he was posthumously anathematized. Anathematized meaning he ceased to become Catholic.
But—note well—in this case Honorius was never deposed. He died in 638 still Pope. He was followed by eight more Popes. Then, 40 years having passed, we got Pope St. Agatho and the condemnation of Honorius.
So in all this forty years, was there anyone arguing that Honorius left his see vacant and all the Popes from Severinus on were not true popes?
You can’t mentally convict a Pope of heresy and then just decide that he is therefore not Pope, or that subsequent Popes are not valid. You may have your personal opinion and that’s fine. But for it to be binding, it has to be done officially and ratified by a Pope and Council, the way the 6th Ecumenical Council anathematized Honorius or the Council of Constance settled the Avignon mess. If Francis or any modern pope needed to be anathematized, it’d have to be by the same process.
And that stands to reason right? Or else every dummy could just go around inventing their own arbitrary papal lines and claimants.