So where did you read it? You should tell us who said so. It sounds like nonsense to me.

We Catholics say the Pope is the leader of the Church and infallible because he is the successor to Saint Peter, the first Pope. However, I have read about an earlier tradition to Papal Primacy....

This is enough to make my head spin.

You forget all the above stuff, it is all wrong.

Christ first built His Kingdom on earth, which is the Roman Catholic Church, on the Rock, Peter the Rock. He then gave the keys to heaven to Peter. Read Mat 16: 18-20

There is no earlier tradition than that.

In the acts of the Ecuмenical Council of Ephesus in the fifth century we read, "There is no doubt, and in fact it has been known in all ages, that the holy and most blessed Peter, prince and head of the Apostles, pillar of the faith, and foundation of the Catholic Church, received the keys of the kingdom from our Lord Jesus Christ, the Saviour and Redeemer of the human race, and that to him was given the power of loosing and binding sins: who down even to to-day and forever both lives and judges in his successors. The holy and most blessed Pope Coelestine, according to due order, is his successor and holds his place." so this is just a pretense the schismatic Greeks use to remain outside Roman Catholic communion. The Fathers of Chalcedon testify, "Peter hath spoken by the mouth of Leo" There is no doubt that the Roman Church is the See of Peter as all the Fathers teach it is, and is indefectible by divine institution. Now, some of the Fathers do indeed sometimes say the Roman Church is also specially protected by St. Paul, and in fact the Roman Pontiffs when anathematizing obstinate heretics from the true Church sometimes invoke the authority of both St. Peter and St. Paul. But, this does nothing to deny the Roman primacy, stemming principally from St. Peter the Apostle - the Greek "Orthodox" have changed the Faith, and denied the primacy of St. Peter.

St. Augustine said, "Number the bishops from the see of Peter itself. And in that order of Fathers see who succeeded whom. That is the rock against which the gates of hell do not prevail." One of the great Greek Fathers of the Church, St. Maximus the confessor bears witness to what the Greek Church faithfully believed and accepted before their schism, "For he only speaks in vain who thinks he ought to persuade or entrap persons like myself, and does not satisfy and implore the blessed Pope of the most holy Church of the Romans, that is, the Apostolic See, which from the incarnate Son of God Himself, and also by all holy synods, according to the holy canons and definitions has received universal and supreme dominion, authority and power of binding and loosing over all the holy Churches of God which are in the whole world." Pope St. Hormisdas, in a formula accepted by the Eastern Churches decreed, In the Apostolic See the Catholic religion has always been kept undefiled and her holy doctrine proclaimed. Desiring, therefore, not to be in the least degree separated from the faith and doctrine of that See, we hope that we may deserve to be in the one communion with you which the Apostolic See preaches, in which is the entire and true solidity of the Christian religion: promising also that the names of those who are cut off from the communion of the Catholic Church, that is, not consentient with the Apostolic See, shall not be recited during the sacred mysteries. and Pope St. Agatho, at the Sixth Ecuмenical Council, which is accepted by the Greek Orthodox said, "This Apostolic Church never turned away from the way of truth nor held any kind of error. This is the rule of faith. All who wish to please God must study to conform the Apostolic rule of the primitive faith founded on the rock Peter, and kept by him from error." St. Jerome likewise says, "My words are spoken to the successor of the fisherman, to the disciple of the cross. As I follow no leader save Christ, so I communicate with none but your blessedness, that is with the chair of Peter.