Jesus placed the authority of the Keys in St. Peter because St. Peter had unwavering faith in Christ revealed by the Father and at the same time had human imperfections. It is significant that each time Peter is elevated or singled out by Christ, Peter's weakness is also brought to mind. In the keys episode St. Peter, unwittingly following Satan, tempts Christ with temporal power. Peter's betrayal is bracketed by Christ's prayer that he remain strong and convert his brethren, and by the charge to feed the sheep.
This prefigures the failings of the human leaders of the Church; it is important for Christ to teach us that His Church is a divine institution infallibly lead by fallible men.
The character of Peter is perhaps best encapsulated in his walking on water, where he is working a miracle as his gaze is on Christ, failing, and calling out to his Savior.