Can you explain the Pope's Infallibility?

When I was a lad, I was told in religious instruction that in matters of faith the pope was infallible. I asked how that had been determined. I was told that this was determined by a/the pope. To me that was a most unsatisfactory answer, i.e., the pope is infallible because he says so and thus being infallible what he says is - - well, infallible. How can I believe such and circular answer and, if I don’t, is it sinful?

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*]In what sense is the Pope Infallible?
*]Papal Infallibility

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