But they are men and it’s possible for them to error, since they are human. I would hope they never would but it’s always a possibility.
Please review the following references from the Catechism of the Catholic Church:
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In order to preserve the Church in the purity of the faith handed on by the apostles, Christ who is the Truth willed to confer on her a share in his own infallibility. By a “supernatural sense of faith” the People of God, under the guidance of the Church’s living Magisterium, "unfailingly adheres to this faith."417
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The mission of the Magisterium is linked to the definitive nature of the covenant established by God with his people in Christ. It is this Magisterium’s task to preserve God’s people from deviations and defections and to guarantee them the objective possibility of professing the true faith without error. Thus, the pastoral duty of the Magisterium is aimed at seeing to it that the People of God abides in the truth that liberates. To fulfill this service, Christ endowed the Church’s shepherds with the charism of infallibility in matters of faith and morals. The exercise of this charism takes several forms:
891 “The Roman Pontiff, head of the college of bishops, enjoys this infallibility in virtue of his office, when, as supreme pastor and teacher of all the faithful - who confirms his brethren in the faith he proclaims by a definitive act a doctrine pertaining to faith or morals. . . . The infallibility promised to the Church is also present in the body of bishops when, together with Peter’s successor, they exercise the supreme Magisterium,” above all in an Ecumenical Council.418 When the Church through its supreme Magisterium proposes a doctrine "for belief as being divinely revealed,"419 and as the teaching of Christ, the definitions "must be adhered to with the obedience of faith."420 This infallibility extends as far as the deposit of divine Revelation itself.421
892 Divine assistance is also given to the successors of the apostles, teaching in communion with the successor of Peter, and, in a particular way, to the bishop of Rome, pastor of the whole Church, when, without arriving at an infallible definition and without pronouncing in a “definitive manner,” they propose in the exercise of the ordinary Magisterium a teaching that leads to better understanding of Revelation in matters of faith and morals. To this ordinary teaching the faithful "are to adhere to it with religious assent"422 which, though distinct from the assent of faith, is nonetheless an extension of it.
Note that there are at least two key components for a teaching to be infallible: the Pope exercises his charism of infallibility when “he proclaims by a definitive act a doctrine pertaining to faith or morals.” The implication is that infallibility is not assumed when he’s issuing statements on matters not related to faith and morals, and hasn’t done so by a definitive act.
In a sense, the charism of infallibility could be viewed as a negative protection - not tha the Pope will always be correct in everything that he says, but rather, that he won’t be incorrect - that is, he will be prevented from teaching error - when he binds the consciences of Catholics on matters of faith and morals (for the power to bind, reference Matthew 16:19).
Infallibility also fulfills the promise of Jesus that he will found a church and “the gates of the netherworld shall not prevail against it.” (Matthew 16:18, NAB). Additionally, it could be viewed as a fulfillment of this promise of Jesus to the disciples: “And behold, I am with you always, until the end of the age.” (Matthew 28:20b, NAB). At the last supper, Jesus made another striking promise to the disciples: “But when he comes, the Spirit of truth, he will guide you into all truth.” (John 16:13, NAB). Without the charism of infallibility, this promise would mean nothing.