The Church teaches that Peter was given primacy amongst the apostles, yet Peter considered himself a “fellow elder” and did not view himself as one superior to the other apostles. So aren’t the local churches to be led by a plurality of elders?
The text, which you cite is 1 Peter 5:1, wherein Peter exhorts the leaders of the Church to be zealous shepherds. But what you see as equivalency may simply be fraternity.
For example, when my Bishop writes a letter to the priests, he begins, “My dear brother Priests…” Now the bishop is a priest, and shares that in common, as a brother, with all the priests of this diocese. But his salutation is not a declaration that there is no difference, or that he does not also have authority over us as the Bishop.
In the letter you cite, Peter begins by writing of himself, Peter, an apostle of Jesus Christ (1 Peter 1:1). Hence your point that he thought of himself merely as a fellow elder does not seem supported.
Further, the Catholic Church’s position on the primacy of Peter does not rise or fall based on one text. Our teaching is based on a number of foundational texts and also on Sacred Tradition.
Thus we see that Christ singles Peter out and calls him “the Rock,” giving him the keys of the Kingdom of heaven, a sign of special authority (Matt 16:19). He also assigns Peter with the special role of uniting the other apostles, when the devil would sift (divide) them like wheat (Lk 22:31-32). Peter is also singled out by Jesus at the lakeside and told to “Tend my Sheep” (John 21).
In Acts we see Peter living the office Christ gave him. He is always listed first among the Apostles. He preaches the first sermon. He convenes the brethren and directs the replacement of Judas. He works the first miracle, pronounces sentence on Ananias and Sapphira, is led by the Spirit to baptize the first Gentiles, and presides over the Council of Jerusalem, bringing unity to its divided deliberations.
Relying not only on a wide biblical tradition, the Catholic Church also bases her understanding of Peter’s office on the broad and consistent testimony of the Fathers of the Church and other witnesses to the practice of Christian antiquity. These sources attest that Peter and his successors were accorded special dignity. Their authority to rule over the whole Church in a unique and singular way is confirmed by these sources.
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