I recently read in Justo Gonzalez' The Story of Christianity, Vol. 2 about the declaration of the First Vatican Council in 1870 concerning papal infallibility. Here's an excerpt:
"Therefore faithfully adhering to the tradition received from the beginning of the Christian faith, for the glory of God our Saviour, the exaltation of the Christian religion, and the salvation of Christian people, the sacred Council approving, we teach and define that it is a dogma divinely revealed: that the Roman Pontiff, when he speaks ex cathedra, that is, when in discharge of the office of pastor and doctor of all Christians, by virtue of his supreme Apostolic authority, he defines a doctrine regarding faith or morals to be held by the universal Church, by the divine assistance promised to him in blessed Peter, is possessed of that divine infallibility with which the divine Redeemer willed that his Church should be endowed for defining doctrine regarding faith or morals; and that therefore such definitions are irreformable of themselves, and not from the consent of the Church" (p. 298).
Wow. I wonder if most Catholic parishioners know that the church believes this, and what they think about it... I mean, even Peter, from whom they derive their authority, was quite undeniably not infallible; Galatians 2:11-14 tells us that he was in serious error and was corrected by Paul.
Personally, I prefer to be labeled "fallible," because I know me, and I know what the book of Romans teaches about fallen humanity. Infallibility is quite a presumptuous claim.