Perhaps the main point the author wants to make is that Peter has been chosen by Jesus to lead the church.
This passage is also interesting because of the different verbs used here for “love” … Jesus asks Peter the first two times, “Do you love me,” using the verb agapaw (altruistic love). Peter responds, “I love you,” using filew (the love of friendship). The third time, however, Jesus himself uses filew, as does Peter.
In a Creighton University Daily Reflection of May 28th, 2004, Robert P. Heaney writes …
Jesus asks Peter: “Do you love me more than these others do?” Peter has, of course, just a few days earlier protested that he would be the last to abandon Jesus, even if all the others deserted. Dreadfully ashamed because he had denied Jesus three times, he doesn’t even try to answer that part of the question. But he ducks the first part as well. He says “Lord you know that I like you.” Then Jesus rephrases the question, dropping the comparison with the other disciples. He said “Simon, do you love me?” Peter recognizes that if he says “love,” he’d be a fraud. So once again he replies “Yes Lord you know I like you.” And then a third time, Jesus asks Peter “Simon, do you like me?” Perhaps we could reread that as “Simon, do you really even like me?” The Gospel tells us that Peter was upset with that third question. It is easy to see why, once we catch the word change. With his first question Jesus challenged Peter’s claim to superior love, and with the second and third, his claim even to love at all. With three simple questions Jesus strips away all of Peter’s defenses. Only then is Peter really able to receive the love that Jesus genuinely offers. This is manifested, in this passage, when, after each question, uncovering layers of self-delusion, Jesus nevertheless entrusts the care of others to Peter: “Feed my lambs, feed my sheep.” God is willing to work with and through human imperfection.
But in his article, Sloppy Agape, Dr. David Alan Black gives the opinion that these differnces come to nought.
Of more interest to me is the relationship between Jesus and Peter. Jesus questions and rebuilds what seemed damaged beyond repair … he dealt with Peter’s earlier denial the way any of us might have dealt with the betrayal of a love that still lived – he asks, “Do you love me?” And when he gets an affirmative answer, he replies, basically, “Prove it.”