So then you disagree with that great Catholic scholar F.A. Sullivan who insists that Apostles were never Bishops and vice versa?
Actually, now that I think about it, being a bishop would be a reduction in rank for an Apostle. Apostles got their authority from Christ, bishops got theirs from the Apostles.
I don't know who F. A. Sullivan is, and don't know why you think I should consider him authoritative.
It is true that the office of Apostle is superior to that of Bishop, so that St. Peter would hold the office of Bishop of Antioch while keeping all of his authority as an Apostle.
As for his position in Antioch, the 1917 Catholic Encyclopedia notes:
The later tradition, which existed as early as the end of the second century (Origen, "Hom. vi in Lucam"; Eusebius, "Hist. Eccl.", III, xxxvi), that Peter founded the Church of Antioch, indicates the fact that he laboured a long period there, and also perhaps that he dwelt there towards the end of his life and then appointed Evodrius, the first of the line of Antiochian bishops, head of the community. This latter view would best explain the tradition referring the foundation of the Church of Antioch to St. Peter.