Infallibility is pretty much irrelevant to the guy in the pew.
This tired old refrain indicates an inability to understand history as well as to ignore the repetitive threads and posts that are confused about infallibility and what teaching is infallible and what is not.
The Church only declared infallibility when Gallicanism became Conciliarism after the Great Western Schism, claiming the superiority of council over the Pope, and promoted by John Gerson (1363-1429) and Peter d’Ailly (1350-1420). The French Revolution drove the bishops into the arms of the Pope and dealt a mortal blow to Gallicanism, but the basic idea was still alive until the First Vatican Council formally condemned it in 1870.
To counter the irrelevant comments we have the revered Fr John A Hardon, S.J.
‘CONCILIARISM. The theory that a general council of the Church is higher in authority than the Pope. It began in the fourteenth century, when respect for the papacy was undermined by confusion in Church and State. William of Ockham (1280-1349), in his battle with Pope John XXII (c. 1249-1334), questioned the divine institution of the primacy. Marsilius of Padua (1324) and John Jandun (1324) declared it was only a primacy of honor. During the great Western Schism (1378-1417) many otherwise reputable theologians, such as Peter of Ailly (1394) and John Gerson (1409) saw in the doctrine of the council’s superiority over the Pope the only means of once more reuniting a divided Church. The viewpoint appeared that the Church in general was free from error, but the Church of Rome could err, and in fact had erred and fallen into heresy. The Council of Constance (1414-18), in its fourth and fifth sessions, declared for the superiority of council over Pope. However, these decisions never received papal approbation. In Gallicanism the conciliarist theory lived on for hundreds of years. Conciliarism was formally condemned by the First Vatican Council (1869-70), which defined papal primacy, declaring that the Pope had “full and supreme jurisdiction over the universal Church, not only in things which belong to faith and morals, but also in those which relate to the discipline and government of the Church spread throughout the world.” He therefore possesses not merely the principal part but “all the fullness of this supreme power.” Moreover, this power is ordinary or constant, and immediate or direct; it extends the Pope’s authority over each and all the churches, whether local or territorial, and over each and all the churches, whether local or territorial, and over each and all the pastors and the faithful (Denzinger, 3063).’
In more recent times, conciliarism has been renewed by those who appeal to a “magisterium of theologians” or “consensus of the people of God” against ordinary or even solemn teachings of the popes. (Etym. Latin concilium, council, assembly for consultation.)
Modern Catholic Dictionary by Fr. John A. Hardon, S.J.