UPDATE: 3/20/13 Please look also at the Catholic explanation and definition of "Infallibility". I am not certain it contradicts this writer's own view of the authority of the church.
In the case of Romanism, this error slowly crept in many centuries ago but took its definite form in the First Vatican Council of 1870. Ironically, as we see, it was a church council which defined this dogma. The contradiction of such a statement is immediately obvious: the Pope was now infallible, but if a council declared it so, then the council itself is infallible also.
Papal infallibility lacks both Scriptural and historical support. It was a complete novelty which scandalized a large sector of Roman Catholicism when it first appeared, and occasioned the separation of the Old Catholics of the See of Utrecht in the Netherlands and its sister churches to this day. Not every Roman Catholic theologian accepts it though not many dare to clearly and openly admit it.
Protestantism, while ridding itself from the shackles of Papal infallibility, has nevertheless fallen into a probably worse and definitely more dangerous error : personal or individual infallibility. In defending the alleged privilege of every individual to privately interpret the Scriptures "under the guidance of the Holy Spirit" it has in fact magnified the Romanist error to the nth degree. The most sacred dogma of Protestantism, "Sola Scriptura", immediately and inescapably brings up the issue of interpretation. "Sola Scriptura", though and attractive and seemingly rational theory has actually never been carried out in real practice. The fact is that the Holy Scriptures need interpretation; to Philip's question to the Ethiopian eunuch: "Indeed, do you know what you are reading?" the answer was: "How can I, except some man should guide me?". Who, then, can interpret Scripture correctly (infallibly)? The Protestant answer is actually twofold. Those subscribing to a more "confessional" position (the Lutherans, the Reformed,etc.) point us to their respective confessions of faith, requiring of their ministers and church officials an absolute allegiance to them. Those of the more "independent" side don't hesitate to defend each individual's right to his own (and unconsciously infallible) interpretation.
The truth lies elsewhere. It lies in Christ's promise that He would build His Church, and that the gates of Hades would not prevail against her; it lies in Christ's promise to His apostles that the Holy Spirit, once come, would guide them unto all Truth. If Jesus is both faithful and capable of fulfilling His promises, and He is then two things must be true: the Church that He founded must still exist today, and only within her borders is the Teaching of the Apostles kept pure and unchanged.
Private infallibility, whether in its Papal or in its Protestant variant, is wrong. Both reflect the arrogance and rebellion of man's fallen state; they are two manifestations of the same disease. Neither Romanism nor Protestantism can possibly provide a cure for this lethal malady.
True infallibility belongs to the Church as a whole. It is found in the Mind of the Church manifested in the consensus of the Fathers, the witness of the countless saints and martyrs throughout the centuries, and the declarations of the Ecumenical Councils. Only the Church is the "the pillar and ground of the truth" as the holy apostle Paul declares. Only within her can a man find the Truth of God's revelation.
Glory to God for all things!
NOTE: Visit Hno. Germán's blog!