For a better understanding of the pope’s role one should read Adrian Fortesque’s "The Early Papacy . . . ", here is an excerpt from that book:
"Anglicans often tell us that all bishops are equal, as if this principle were an objection to the papacy. So they are, as far as the order of the episcopate is concerned. There is only one order of bishops; no one can be, in any sense, more a bishop than another. If a man is ordained Bishop of Rome, he receives exactly the same sacrament as ne who is ordained bishop of the smallest suffragan see in the most remote land. The bishop of Rome, as far as order goes, is no more a bishop than the bishop of Krishnagar. But all bishops are NOT equal, in the sense that none has authority over any other. In this sense the statement is false and can be proved to be false from the very beginning of the Church history. It can be proved false by other examples than that of Rome. From the beginning there have been cases of bishops who had EXTRADIOCESAN authority, that is, jurisdiction, real jurisdiction, over their fellow bishops. To this day the Anglican must be familiar with the idea of an archbishop, who has authority outside his own diocese over other bishops, though these do not thereby cease to be real ordinaries and do not become merely his auxiliaries. Over archbishops, there were still, in some cases, primates, sometimes over primates such great people as exarchs. . . . In the first six centuries it was a very solid authority. Over archbishops, primates, and exarchs stand those greatest bishops of all: the five patriarchs. Their authority was always, is still, very great indeed. It is seen only in the East, because there is but one patriarch in the West, who is the Pope himself. But the principle is there; it should help anyone who has difficulties to understand at least the possibility of the Pope’s jurisdiction over than bishops. The point that seems to make all the difference in appreciating the Pope’s position is that this is not an isolated fact. The papacy is the topmost point of a regularly graduated hierarchy of bishops, in which each has authority over those under him. . . .
Or is there something specially impossible in the idea of a man having authority over other bishops, successors of the apostles as he is himself? Then how about the jurisdiction of an archbishop, a primate or a patriarch? But Christ is the head of the Church (cf. Col 1:18). Of course he is. He is the head of each diocese, too, the head of each province and patriarchate. If he can have a visible vicar to represent his authority over the diocese and patriarchate, what difficulty is there against the idea of a still higher vicar of Christ, representing his authority over all? We know that Christ governs, teaches and sanctifies his Church through men, his vicars. Christ baptizes; Christ consecrates; Christ forgives sins; he rules the diocese. Christ rules the whole body, too, at headquarters; here, too, he does so through his minister. . . . The pope is not, in the absolute sense, head of the Church; the head of the Church is Jesus Christ, our Lord, as our English catechism says. The Pope is the vicar of that head and is therefore the visible head of the Church on earth, having authority delegated from Christ over the Church on earth only, just as every diocesan bishop has authority delegated from Christ over his diocese only."
). I am not saying that is necessarily bad (I don’t really like popular apologetics, but I guess it has its place), but it perhaps explains why we always seem to talk past each other