No such thing as a bad pope, just bad people.

Many people try to disprove the accuracy of the Church's teachings by calling out sinful popes. Nobody is perfect, neither are the popes. This argument of bad popes does distinguish infallibility and impeccability. There were pope who were not celibate, or they used their power for the wrong reasons, but none of them declared incorrect doctrine. The go to example of a "bad" pope is Pope Honorius, people said he taught Monothelitism which describes as only divine. When he was settling the controversy, he thought to not do anything at all. This shows the infallibility of the Pope because even when Honorius was teaching Monothelitism, he did not define it as doctrine so there would be peace in the Church. By not defining Monothelitism as truth, Honorius showed that the office of the papacy is infallible when defining doctine.