In discussing the teaching authority — the magisterium — of the Church, most people put up resistance to the idea that any single man or collection of men can be held infallible. This even holds true for many Catholics, whether their dissent is religiously conservative (SSPX) or liberal (Catholics For Choice).
But as we remember from “The sola scriptura problems”, Jesus promised the guidance of the Holy Spirit to the Church (Jn 14:26, 16:13). If we hold the Holy Spirit — God — to be trustworthy and reliable (Rom 3:3-4; 2 Tim 2:13), then that guidance must necessarily impart infallibility to the Church’s teachings. And, indeed, St. Paul calls the Church “the pillar and foundation of truth” (1 Tim 3:15). Nor can the Church lose that guidance without breaking Christ’s other promise: “And surely, I am with you always, to the very end of the age” (Mt 28:10 NIV).
Let’s consider it from another angle: Infallibility, in doctrinal terms, functions much like the American judicial principle of stare decisis (“let the decision stand”). Under stare decisis, lower courts aren’t free to controvert decisions of upper courts, especially not those of the Supreme Court. The only difference is, while SCOTUS holds itself able to overrule previous decisions at its own level, infallibility goes forward in time to bind future councils and popes: Pope Benedict could no more dispense with the doctrine of the Immaculate Conception than he could overrule the doctrine of the Trinity.