It's only infallible when it's the message you want to hear. If the message isn't to your liking then it must be the work of the devil. Very similar to "he's not hurting the right people".
Indeed. I was trying to (probably too obliquely) highlight how futile it is to inject any logic or reasoning into the situation, given the subject matter.
...We teach and define that it is a dogma divinely revealed that the Roman pontiff when he speaks ex cathedra, that is when in discharge of the office of pastor and doctor of all Christians, by virtue of his supreme Apostolic authority, he defines a doctrine regarding faith or morals to be held by the universal Church, by the Divine assistance promised to him in blessed Peter, is possessed of that infallibility with which the divine Redeemer willed that his Church should be endowed in defining doctrine regarding faith or morals, and that therefore such definitions of the Roman pontiff are of themselves, and not from the consent of the Church, irreformable.
Sounds pretty cut and dried to me. It applies whenever the Pope speaks ex cathedra, and the bishop was directly contravening such doctrine regarding faith or morals.
The literature about this subject is all over the place. I definitely see no consensus that there have only been two. Maybe two that are very good examples, but the general theme is that whenever he speaks of faith or morals he is infallible. Oh well, you could spend a lifetime trying to logic the illogical.