Well, Paul clearly was superior to Peter in some respects. Peter was just a shepherd, feeding sheep, feeding lambs, feeding sheep. Just a shepherd, after all. V's wife.
1Pe 5:1 The elders which are among you I exhort, who am also an elder, and a witness of the sufferings of Christ, and also a partaker of the glory that shall be revealed:
1Pe 5:2 Feed the flock of God which is among you, taking the oversight thereof, not by constraint, but willingly; not for filthy lucre, but of a ready mind;
All the elders of the church were instructed to feed the sheep...And if you think it meant supremacy for Peter, look at the next verse...
1Pe 5:3 Neither as being lords over God's heritage, but being examples to the flock.
Well that shot the primacy of Peter to pieces, and anyone after him that thinks they are any more than a sinner in God's church, including any of the so-called 'church fathers' who demand that the followers esteem the bishops more highly than or even equal to the scripture...
That bible will straighten out kinds of mis-understanding...