One of my beefs with Bible professors (and I am one of them) is that sometimes we take a perverse delight in skewering common misinterpretations of Scripture, but then we leave people with nothing. We take away meaning, rather than adding understanding. My goal, as a professor who regularly skewers bad interpretation, is to replace bad interpretation with better - and that better interpretation is (or ought to be) more attractive because it is truer and more powerful.
In John 21:15-17, there is much to learn after we remove bad interpretation. First, we find seven disciples fishing. Since fishing was not primarily for recreation, it seems that Peter is returning to his old career. Nothing wrong with fishing for a living - but Peter had been called to be a full-time disciple of the rabbi. Peter probably felt that his failure disqualified him to serve or lead.
The miraculous catch of fish in John 21 is a reminder of Peter's initial call to be a "fisher of men." (Nerd note: this version of Peter's initial call is found only in Luke 5:1-11, and not in John. But I think that we have here an example of what Johannine scholars call "interlocking," where John refers to things that the readers would only know if they were familiar with the Synoptic gospel stories, and especially Luke). The repeat of the miracle puts Peter in a state of mind to be re-summoned to service.
The miracle also contains a minor allusion to an OT prophecy about the new covenant age. Ezek 47:1-12 describes a river of healing water flowing from the Temple (compare to John 7:37-39, where the river comes from Jesus), which bring a multiplication of fish. Some ancient rabbinic sources specifically located Ezekiel's multiplication of the fish at the Sea of Tiberias (cp. John 21:1).
Jesus further prepares Peter for restoration by cooking breakfast over an anthrakia, a charcoal fire, perhaps in a metal brazier. The only other time that anthrakia occurs in the Bible is in John 18:18, where Peter denied that he knew Christ three times. This explains the repetition in John 21. Peter now has the chance to do it right. Just as three times he denied Jesus before enemies, he now can affirm his love for Jesus three times before friends.
Jesus' goal is to restore Peter to self-sacrificial service, to help him become a shepherd like Jesus (see John 1o). Part of the reason that Peter had denied Jesus was that he had wanted to die with Jesus, and followed Jesus into a place where he was unable to remain loyal. He was more concerned with his own personal loyalty to Jesus, and less concerned with shepherding his brothers.
Peter took his re-appointment to shepherding seriously. Thirty years later, he wrote this to church leaders: "Shepherd the flock of God among you, not grudgingly, but willingly, as God wants you to... be examples to the flock. Then when the Chief Shepherd appears, you will receive a glorious and unfading crown." (1 Pet 5:2-4)