Dear brother JSMelkiteOrthodoxy,
Firstly, what Jesus gave to Peter he also later gave to all of the apostles.
No, he only gave to Peter the keys, but gave to all the power to bind and loose. That's what the biblical text says.
Secondly, Rome does not have a monopoly on Peter. At least three sees can claim St. Peter
This is true, but according to Apostolic Canon 34, the head bishop must still be recognized and heeded, and this was clearly the bishop of Rome in the early Church.
and the majority of the fathers taught that it was Peter's confession upon which the Church was built, not necessarily Peter himself.
The non-Catholic argument confuses the person of Simon with the person of Peter. Peter is intimately bound to his confession and was given by a
singular grace from God Himself, and
was not given to the other Apostles. Without the confession, Peter would not exist, and vice-versa. Remember, don't confuse the person of Simon with the person of Peter, which is a special grace from God for the edification of His Church.
The ancient Church of Rome was not founded by Peter but gained prestige because of the martyrdoms of Peter and Paul. Because of this and because it was the old capitol of the Roman empire, the Roman Church had great prestige and so enjoyed a primacy of honor.
By virtue of your first sentence
alone, the Church of Rome gained precedence in the early Church, and for no other reason. Apostolicity was the hallmark of a Church's greatness, not its civil status. This false claim was rightly contested by the Sees of Rome and Alexandria. The Church of Constantinople resisted the truth for a while, but even her political influence could not cover the truth that the Church of Rome was teaching. By the time of the Trullan Council, the Church of Constantinople no longer claimed her prestige due to a side-effect of civil status. Rather, in the Sixth century, we find that she finally comes around and claims her prestige due to apostolicity (from St. Andrew), as Rome had always insisted. Thus it is that in the Council deemed the Eighth Ecumenical by the Latin Church, the Pope accepted Constantinople's claim as the Second See. Unfortunately, the Easterns repudiated this Council, and polemic Orthodox revisionism claims that the Latin Church did not accept Constantinople as the Second See only until the establishment of the Latin Kingdom in the Middle East, and this by virtue of mere political expedience (and that's just a lie, to be perfectly blunt).
Blessings,
Marduk