I would suggest you bone up on the doctrine of papal infallibility. it has nothing to do with the pope not being a human being, a sinner and someone who makes mistakes.
you are correct on clerical celibacy.
I am familiar with the concept of papal infallibility. I know that it does not apply to everything the Pope says or does. I also know that instituted by Pope Pius IX in the late 19th century. It is a doctrine I simply don’t agree with. I think popes are capable of error, even matters of theology.