Its existence through the Holy Father is unique to Catholicism and this fine article from Catholic Culture explains.
“Recently a very intelligent layman asked me why I had written somewhere that Anglicanism had no “authority principle”, when in fact the Anglicans do have bishops, including the Archbishop of Canterbury. For years I have referred to Catholicism’s “authority principle” as something unique and essential to revealed religion. Now, suddenly, I doubted whether some of my readers really knew what I was talking about.
“Let us suppose God wishes to reveal Himself to us in a way which gives us not just an experience of the Divine but a formal knowledge of God, His nature, His purposes, and His commands. He wants, in fact, to establish a religion based on these things, a religion which can be truthfully taught, so as to bring men into conformity with Himself. Now let us suppose that this Revelation is delivered in some way. Never mind, in this essay, whether the manner in which He reveals Himself is objectively verifiable and broadly witnessed. That is not our concern at present. However He does it, there will be some revealed content which the human community receives. This content may be immediately written (think of the Ten Commandments); or it may be something taught by God’s anointed representative, whose teaching are then preserved over time.
“However it is done, the precise interpretation of this revealed content can be guaranteed only as long as the Revelation includes some designated mechanism to preserve and protect it and to oversee the legitimate developments of its leading ideas as new questions arise. This is what is called an “authority principle” in religion. Either a Revelation contains such a mechanism, preserved within the religion it engenders, or it does not. And unless this principle is divinely guaranteed to produce infallible results with respect to the issues on which the Revelation is authoritative, then there is no guarantee that the Revelation will be understood in the same way by future generations.
“The result of the absence of an authority principle is that a Revelation must ultimately fail of its purpose over time. Yet this can hardly be what God intends. Therefore, we ought to expect that an authentic Revelation will contain an authority principle within it, and this expectation ought to be so strong that the absence of an authority principle will substantially weaken the case for the authenticity of an alleged revelation or of any religion which claims to be based upon it.
“Catholicism’s Authority Principle
“It is in this sense that the claim of Catholicism to a Revelation with an authority principle, which it carries on through time, is so striking, especially in the absence of a similar claim in any other religion yet known to man. Note here that the existence of an authority principle is not to be confused with the existence of leadership. All religions have leaders; some even have bishops. But only Catholicism claims that its founding Revelation contains within it a mechanism for infallibly interpreting, developing and applying the content of the Revelation over time, long after the “revelation event” has passed.
“The authority principle in Catholicism ensures that there is no difference in dispensation between the first Christians and ourselves, such that they should have had a living, infallible guide to the truth (in Christ) and we have not. Thus Peter and His successors have been commissioned by Christ as His vicars, with the authority to bind and loose, the exercise of the keys to the Kingdom of Heaven (Mt 16:18-19), and the ability to confirm their brethren in the faith (Lk 22:32). This is all based on Christ’s prayer that Peter’s faith would not fail (again, Lk 22:32).”