Interesting document here:
Although the New Testament gives us limited information about the historical career of Simon Peter, individual writings associate him with different aspects or images of Ministry which have relevance to the church as a whole. It is Peter among the Twelve who confesses Jesus as the Christ (Mark 8, Matthew 16, Luke 9) and as the Holy One of God (John 6); he is listed as the first apostolic witness to the risen Lord (1 Corinthians 15; Luke 24); he is the rock on which the church is to be founded and he is to be entrusted with the power of the keys (Matthew 16); he is the one who is to strengthen his brethren in faith (Luke 22); he is the one who, after confessing his love, is told to feed Jesus’ sheep (John 21); he takes the initiative in filling the vacancy among the Twelve (Acts 1) and receives the first Gentile converts (Acts 10). He is also the one who denies Jesus in an especially dramatic way (all four Gospels); who sinks in the waves because of his lack of faith (Matthew 14); he is sharply rebuked by Jesus (Mark 8, Matthew 16), and later on by Paul (Galatians 2). The fact that these failures were so vividly remembered is perhaps also evidence of his prominence.
(13) How this view of Peter in the New Testament as developed by modern scholarship relates to the papacy might be summarized thus. Peter was very important as a companion of Jesus during Jesus’ public ministry; he was one of the first of the disciples to be called and seems to have been the most prominent among the regular companions. This importance carried over into the early Palestinian church, as indicated in the record of an appearance of the risen Jesus to Peter (probably the first appearance to an apostle). Clearly he was the most prominent of the Twelve and took an active part in the Christian missionary movement. Peter had a key role in decisions that affected the course of the church. Thus one may speak of a prominence that can be traced back to Peter’s relationship to Jesus in his public ministry and as the risen Lord.
Of even greater importance, however, is the thrust of the images associated with Peter in the later New Testament books, many of them written after his death. While some of these images recall his failures (e.g., Peter the weak and sinful man), Peter is portrayed as the fisherman (Luke 5, John 21), as the shepherd of the sheep of Christ (John 21), as a presbyter who addresses other presbyters (1 Peter 5:1); as proclaimer of faith in Jesus the Son of God (Matthew 16:16-17); as a receiver of special revelation (Acts 10:9-16); as one who can correct those who misunderstand the thought of a brother apostle, Paul (2 Peter 3:15-16); and as the rock on which the church was to be built (Matthew 16:18). When a “trajectory” of these images is traced, we find indications of a development from earlier to later images. This development of images does not constitute papacy in its later technical sense, but one can see the possibility of an orientation in that direction, when shaped by favoring factors in the subsequent church. The question whether Jesus appointed Peter the first pope has shifted in modern scholarship to the question of the extent to which the subsequent use of the images of Peter in reference to the papacy is consistent with the thrust of the New Testament.