Mary’s cousin said that, not Jesus, and in Mary’s own prayer in Luke she admits she needs a savior. sinless people don’t need saving or a savior.
and describing the authority given to men does not prove papal infallibility.
you seem to forget peter was harshly rebuked by paul for sliding back into legalism, apparently not an infallible first pope.
Mary's cousin didn't say that...it was the angel at the Annunciation....Peter being rebuked has nothing to do with anything and Paul was certainly not in authority to have a say over the person whom had been given the Keys to the kingdom of Heaven....Christ instituted one Christian church....not 20,000 denominations, and He promised to be with her until the end of time......close enough for me!!!