I like Peter because I am so like Peter. As I meditate on John 13, I see a man who thinks he knows it all when he knows nothing at all. Peter protests the washing of his feet even though Jesus tells him he doesn't understand. Peter replies (13:8) with a passionate "Never may you wash my feet forever" (εις τον αιωνα). It is a "forever" denial driven by an ignorant zeal. Jesus gently corrects him, "If I do not wash you, you have no part with me" (13:8).
The "me" (εμου) is emphatic and the "with me" (μετ' εμου) indicates Jesus is talking about communion not union. Jesus does not say, "You have no part in (εν) me." which would have suggested salvation. He says, "you have no part with (μετ') me." Jesus is talking about the intimacy of true friendship. A follower of Jesus can miss out on closeness with Jesus through the pride of ignorant passion.
To have a part with Jesus is to share in His ministry. It is "to be his partner, to share in his work" (Bernard, St. John, 2:461). To have a part with Jesus is also to share a friendship with Him. The word is used in the story of Mary and Martha (Luke 10:42) when Jesus tells Martha, "Mary has chosen the good part, which shall not be taken away from her." The good part is the intimacy of true friendship with Jesus that only comes by letting Jesus serve us - letting Jesus wash our feet. Our service for Jesus can become a substitute for intimacy with Jesus.
I like Peter because he catches the point even while missing the truth. Peter immediately asks Jesus to wash not just his feet but also his hands and his head (13:9). He is filled with passionate loyalty, but he still won't let Jesus do as He pleases. It is possible to be very devoted to the Lord yet very wrong at the same time. I, too, feel that temptation to substitute ministry for intimacy and miss the depths of love Jesus longs to share with me.