Infallibility! Ah yes - but they often got that wrong didn't they! Remember the infallible Pope who declared that the crossbow, the world's most lethal weapon at the time, could not be used against Christians but only against Muslims because they were inferior both morally and religiously. Remember the Pope who declared that  native South Americans were animals and so they could be slaughtered in order that the Spanish and Portuguese could steal their lands. Remember the Pope who declared that black Africans had no souls and so they could be used as slaves in the colonies to benefit the wealth of the Jesuit sugar plantations! Get educated about infallibility!