Among Catholic doctrines, those pertaining to the papacy tend to be the most misunderstood and contested by non-catholics. The following verses show the biblical basis for Catholic teaching on the primacy of Peter, the office of the papacy being established by Christ and allusions to the doctrine of infallibility. These doctrines reached their full development in the life of the Church only after centuries of contemplation and study, in councils and through the actions of the popes. And we should never forget that since the Church is likened by Christ to a mustart seed that grows and develops organically from a speck into a large treelike plant, therefore we should not expect to see the Churchs doctrines fully developed and visible in its present form in the pages of the New Testament. What we do find in the New Testament though, is the scriptural record of Peters primacy among the Apostles and the seminal outlines of the doctrines pertaining to the papacy.
One compelling biblical fact that points clearly to Simon Peters primacy among the 12 Apostles and his importance and centrality to the drama of Christs earthly ministry, is that he is mentioned by name (e.g. Simon, Peter, Cephas, Kephas, etc.) 195 times in the course of the New Testament. The next most often-mentioned Apostle is St. John, who is mentioned a mere 29 times. After John, in descending order, the frequency of the other Apostles being mentioned by name trails off rapidly.
When the names of all the Apostles are listed, Peter is always first. Judas Iscariot, the Lords traitor, is always listed last (cf. Matt. 10:2-5; Mark 3:16-19; Luke 6:14-17; and Acts 1:13). Sometimes Scripture speaks simply of Simon Peter and the rest of the Apostles or Peter and his companions (cf. Luke 9:32; Mark 16:7; Acts 2:37), showing that he had a special role that represented the entire apostolic college. Often, Scripture shows Simon Peter as spokesman for the entire apostolic college, as if he were the voice of the Church (cf. Mat. 18:21; Mark 8:29; Luke 8:45; Luke 12:41; John 6:68-69).
Actually, as someone pointed out on another thread, according to Acts 15 it was James who ran the Jerusalem Council, not Peter. Peter was there and played a supporting role (Acts 15:7) but it was James who rendered the verdict (Acts 15:13). Now if Peter was the leader of the Church, sitting in judgment, one has to wonder why James would be the one to make the final decision? The only conclusion one can come to based upon scripture is that James led the early church.