Scenario 1: The Pope is accused of heresy. A group of Bishops, priests, and theologians — along with the usual collection of bloggers and video-making enthusiasts — issue a “formal correction” and they demand, in a filial way of course, that the Pope “repent”.
The Pope ignores them. Then they issue the second correction, as Saint Paul suggests. The Pope does not “repent”. So they publicly claim that he is deposed.
But the Pope continues to ignore them. He in fact remains on the See of Peter, and he continues to exercise papal authority. Deposition failed.
Scenario 2: The papal critics accuse the Pope of heresy. They issue a document which many persons sign. They loudly proclaim his guilty to the world. They establish a commission to examine the accusation, which confirms his teaching is heresy.
The Pope responds by defining his own teaching as dogma under Papal Infallibility, and by defining their position as heresy.
His teaching under Papal Infallibility cannot be wrong. They have no claim to infallibility. They are established as the ones who are heretics.
Scenario 3: Pope Francis restricts the Latin Mass, and makes rules requiring all priests to concelebrate and to say the Novus Ordo Mass every so often. This is a hypothetical, at this point in time.
The Latin Mass traditionalists break communion with the Pope and the body of Bishops, and they set out on their own, like the son who took his father’s inheritance and set out on his own.
They will end up with no Pope, no principle of unity. They will become divided into ever smaller groups. They will not agree among themselves on what is correct doctrine, and they have no Pope to settle their disagreements. Many of their followers fall away from the Faith altogether.
Popes cannot teach or commit heresy; they cannot fail in faith by apostasy or idolatry; they cannot err gravely in doctrine or discipline. All this is clearly established in my book. So if you are certain that the Pope has erred gravely, or is guilty of apostasy, heresy, or idolatry — you are certainly the one who is wrong.