To Jason:
Wolseley has touched on this topic in the past, so I'll give it a try, if us old duffers have any memory left, LOL.
Paul reprimanded Peter in terms of CONDUCT, not of teaching or belief. Think of it along the lines of Paul telling Peter to get his elbows off the table, or not to pick his nose in public.
As for your other question, I've encountered this in Apologetics. Folks like to point a finger and say, "Hey, PAUL was the one traveling all over, establishing Churches, and writing all those Scriptures!"
First, I doubt sincerely whether Paul actually picked up a pen and thought, "Today, God and I are going to write a book for the New Testament." Paul had heard of problems in the baby churches, and he was writing to them to correct them. His corrections are applicable to us, even today, and we should thank the Holy Spirit for preserving Paul's letters for us.
But the Bible isn't a popularity contest: He who writes the most, wins. Remember, Jesus never wrote ANYTHING, except some scribbles in the dust which were eventually rubbed away!
To illustrate the position of Peter in the New Church, look at the Gospels, first. Of course, there is where Jesus renamed Simon to Rock, and gave him the Keys to the Kingdom of Heaven. But read the parts about after the Resurrection, in those precious days before Jesus returned to the Father. MOST important, see that even though Peter denied Christ three times before the Crucifixion, Jesus didn't go stomping up to Peter and say, "You blew it, Buddy. Give Me back those Keys." No, instead, Jesus asks Peter three times if Peter loves Him. And He directs Peter to care for His sheep. Jesus is the Good Shepherd, and He was making sure the "sheep" would be cared for after He returned to the Father.
The most profound and yet still very subtle indication of Peter's leadership, though, is in the book of Acts. Read through it VERY carefully, and take note of each time the Apostles are mentioned by name.
Which Apostle is ALWAYS named first?
GREAT stuff!
Peace,
~VOW