Vatican Embassy Protestor

[Purplundy]

In principle, the Cardinals are selected infallibly by the Pope who, in turn, infallibly select the bishops and so on.

No, they're not. That is exactly what the Catholic Church doesn't teach. But if you want to hold that ground, you'll have to come up with some proof.

If the hierarchy can fail, in process or action, the Pope is fallible.

Yeah, he is. Sometimes, he forgets his car keys. But the Catholic Church holds that its teaching (what is written down in the Catechism) is infallible, so when the Pope decides to add something to that, he is infallible. And that doesn't happen often.