There is only one Truth. Only God has a lock on it. The dark glass of sin obscures much of it from fallen man. I would be arrogant to claim I am perfect and infallible (probably even blasphemous), yet your church makes these claims despite its history of errors. Every hundred years or so it must have a new issuance of papal bulls, council edicts or Vatican conferences to try to restate or "clarify" obvious wrongs. I could point out some of these but what's the use? Your church does fancy footwork with words to "explain" it away rather than face what is plainly evident.
Infallibility is not the absence of sin. Nor is it a charism that belongs only to the pope. Indeed, infallibility also belongs to the body of bishops as a whole, when, in doctrinal unity with the pope, they solemnly teach a doctrine as true. We have this from Jesus himself, who promised the apostles and their successors the bishops, the magisterium of the Church: "He who hears you hears me" (Luke 10:16), and "Whatever you bind on earth shall be bound in heaven" (Matt. 18:18).
Vatican II explained the doctrine of infallibility as follows: "Although the individual bishops do not enjoy the prerogative of infallibility, they can nevertheless proclaim Christ’s doctrine infallibly. This is so, even when they are dispersed around the world, provided that while maintaining the bond of unity among themselves and with Peter’s successor, and while teaching authentically on a matter of faith or morals, they concur in a single viewpoint as the one which must be held conclusively. This authority is even more clearly verified when, gathered together in an ecumenical council, they are teachers and judges of faith and morals for the universal Church. Their definitions must then be adhered to with the submission of faith" (Lumen Gentium 25).
Infallibility belongs in a special way to the pope as head of the bishops (Matt. 16:17–19; John 21:15–17). As Vatican II remarked, it is a charism the pope "enjoys in virtue of his office, when, as the supreme shepherd and teacher of all the faithful, who confirms his brethren in their faith (Luke 22:32), he proclaims by a definitive act some doctrine of faith or morals. Therefore his definitions, of themselves, and not from the consent of the Church, are justly held irreformable, for they are pronounced with the assistance of the Holy Spirit, an assistance promised to him in blessed Peter."
The infallibility of the pope is not a doctrine that suddenly appeared in Church teaching; rather, it is a doctrine which was implicit in the early Church. It is only our understanding of infallibility which has developed and been more clearly understood over time. In fact, the doctrine of infallibility is implicit in these Petrine texts: John 21:15–17 ("Feed my sheep . . . "), Luke 22:32 ("I have prayed for you that your faith may not fail"), and Matthew 16:18 ("You are Peter . . . ").
It is the Holy Spirit who prevents the pope from officially teaching error, and this charism follows necessarily from the existence of the Church itself. If, as Christ promised, the gates of hell will not prevail against the Church then it must be protected from fundamentally falling into error and thus away from Christ. It must prove itself to be a perfectly steady guide in matters pertaining to salvation.
Now that you have a clearer understanding of papal infallibility, please cite as many examples as you choose of errors in teachings on a matter of faith or morals.