Correction. The Evangelical Catholic faith.
Sorry, Peter. Couldn’t resist.
The Faith built on the Apostles.
Hebews11:
39 And all these, though well attested by their faith, did not receive what was promised, 40 since God had foreseen something better for us, that apart from us they should not be made perfect
So then, why would even the apostles need to Confirm their Gospel through Peter?
Paul and the Other Apostles
2 Then after fourteen years I went up again to Jerusalem with Barnabas, taking Titus along with me. 2 I went up by revelation; and I laid before them (but privately before those who were of repute) the gospel which I preach among the Gentiles, lest somehow I should be running or had run in vain. 3 But even Titus, who was with me, was not compelled to be circumcised, though he was a Greek. 4 But because of false brethren secretly brought in, who slipped in to spy out our freedom which we have in Christ Jesus, that they might bring us into bondage— 5 to them we did not yield submission even for a moment, that the truth of the gospel might be preserved for you. 6 And from those who were reputed to be something (what they were makes no difference to me; God shows no partiality)—those, I say, who were of repute added nothing to me; 7 but on the contrary, when they saw that I had been entrusted with the gospel to the uncircumcised, just as Peter had been entrusted with the gospel to the circumcised 8 (for he who worked through Peter for the mission to the circumcised worked through me also for the Gentiles), 9 and when they perceived the grace that was given to me, James and Cephas and John, who were reputed to be pillars, gave to me and Barnabas the right hand of fellowship, that we should go to the Gentiles and they to the circumcised; 10 only they would have us remember the poor, which very thing I was eager to do.
Here, we see that Peter is mentioned with John as having authority even though James was the Overseer of the Church in Jerusalem.
But what is evident, is that there was unity among these three, so Paul does not distinguish Peter as excercising his prime authority. But in Acts, there seems to be a more distiguished authority expressed through Peter. He stands up and ends the debate.
I think Paul paints the picture a little different than Luke, because he was compelled to express the equally important aspect of behaving in accordance with the Gospel which we preach. But it is obvious that Paul sought Jesus’ Confirmation by going to the “pillars”. He happened to be quite confident in his preaching, and for good reason because he was right. But He was also humble, because he knew that Jesus established an order of leadership for the sake of peace and unity.