While Peter was a good friend of Jesus, the fact that he often slipped into a very skewed view of the Gospel is spelled out plainly in Paul’s letter to the Galatians. He had a tendency to hide in his Jewishness and was soundly (and publicly) rebuked by Paul, the apostle sent to the Gentiles (that’s you and me). Check Paul’s letter to the Roman believers and see if you find any trace of Peter’s supremacy...I find only Jesus. But, if you need to have some sort of “worldly organization” to feel safe, I leave you to that. But, out here, out of the camp, with Jesus, there is freedom and light and safety.
There's no evidence whatsoever that ANY of the Apostles were appointed on the basis of merit: certainly not Peter, an impetuous man whose failings are all there in the honest chronicle of Scripture. Yet his threefold denial of Christ, so plainly and painfully recounted in the Gospel, culminated in his threefold reassertion of his love of Christ, and then Jesus' threefold commissioning of him to his new vocation as shepherd of Christ's whole flock: "Feed my lambs, Feed my lambs, Feed my sheep." (John 21:15)
This doesn't make Peter impeccable. It does make his chief shepherd of the flock after the Lord ascends on high. Correction he still needs, as do we all; sometimes a face-to-face confrontation he needs; but he is shepherd nevertheless, and thus will not (even despite his faults) lead the whole flock off a cliff of false doctrine.