It seems to me that the final statement in John 20.30-31 is not the end of an “original” Gospel, but is, instead, a natural summary of other things Christ did when he was newly resurrected in front of, or for, his disciples: for their benefit. But not only just after His resurrection: the statement in v 30 seems to indicate that there were many other things John hasn’t included in his Gospel that Christ did during His ministry on earth: John says, in v 31 that he has only included what he has written so that the reader may believe that Jesus is the Christ, the Son of God, so that the reader may have life in Christ’s name. This is the second of three appearances of Jesus to the disciples, and in chapter 20, they have all seen Jesus resurrected, believe that and that He is the Christ.
John 21 deals with the third of the appearances of Christ after his Resurrection. It deals with Peter not because it was a papist addition, meant to justify the assertions of those who sat in the seat of Peter as leader of Christendom. It deals with Peter because he denied Christ. This denial was similar to the treachery of Judas–both denied the Saviour of the world. The difference between them is that Peter realized his error, and was sorry for it, whilst Judas did not, despaired, and committed suicide. And just as one of the two thieves crucified with Christ repented and asked forgiveness for his sins, thus did Peter likewise, but Judas didn’t. Judas could have, but wouldn’t, and that was foreseen by God at the very beginning of Creation.
So Peter must be forgiven too, just like the one thief on the cross. He still loves and believes that Jesus is the Christ. Peter’s sin of denial wasn’t a lack of faith, but a lack of nerve when he was personally and publically endangered because of his faith. And so Jesus’ act of forgiveness of Peter is an act of instruction and correction too, which Peter will take to heart.
Even if the whole religion of Christ was wholly invented by the, which it isn’t, the denial of Peter and its similarities and differences to the denial of Judas, would leave the Gospel of John with an intolerable loose-end. To John, writer of the truth of the History of Jesus, and inspired by the Holy Spirit to do so, leaving such a loose-end as the unresolved denial of Christ by Peter would be unconscionable. It would be impossible because the Holy Spirit would certainly remind him of it. So John records the third time Jesus appeared to them after His resurrection, because what John records actually happened. The forgiveness of Peter and the raising of his status among the Twelve ends the Gospel perfectly, a Gospel that records, early on, Jesus saying in John 3:16-17:
16 For God so loved the world that He gave His only begotten Son, that whoever believes in Him should not perish but have everlasting life. 17 For God did not send His Son into the world so that He might condemn the world, but that the world through Him might be saved.
Proud and braggadocios, but committed Peter needed to experience his limitations, recognize his need, and accept the salvation and exaltation from Jesus that God had planned for him from before the beginning of time. It was a fitting end to a book that began with a profound statement of mankind’s hopeless condition: trapped in sin and dark despair of unknowing: “And the light shines in the darkness, and the darkness did not apprehend it” (John 1.5).
But Peter apprehended it, and Judas. But Peter repented, and Judas didn’t.
Also, one of the comments on this page notes that John’s Gospel was not cited by the early church fathers until the end of the 2nd century A.D., and because of that, some think that the book was kept secret or privately localized. One implication derived from that was that it is possible that the book wasn’t a finished edition until the end of the 2nd century, long after John’s death.
My answer to this absurdity of baseless rationalization is what translators already know about ancient manuscripts: many were lost. It cannot be asserted with any confidence that the early church fathers didn’t cite from the Gospel of John, nor that they were unaware of its existence, either because the book was kept secret like Daniel’s was, nor because it was privately localized until after the 2nd Century.
For one thing, so many ancient writings were lost to the ravages of history, we cannot say with any certainty that the early church fathers didn’t know of and cite the Gospel of John. Even the spurious and likely Gnostic Alexandrian texts weren’t known for 20 centuries, and it may be possible to someday find examples where the early church fathers did indeed cite from the Gospel of John–to assert with certainty that they never did in order to buttress a theory is bad historical technique, at least at this point–and bad theorizing.
For another, of all the Gospel writers an ancient church father would read, which one would he be least likely to cite from memory? Surely the one by the hand of he who wrote curses in another work condemning those who added or subtracted from the words of the Great Revelation. Even more so because to add or subtract from the message of that text was one thing, but to add or subtract, even by mistake, from the very words and history of the Saviour contained in John’s Gospel was even more serious a proposition. These verses (Revelation 22.18-19) were written by John specifically to counteract Gnostic teachings, who altered the texts of the New Testament writers to fit their presuppositions, not the actual teachings of Christ. The early church fathers knew this, and would naturally have applied the principle to the Gospel of John, for he was a witness to the life of Christ, and so what he says in his Gospel, since it differs from the synoptics, has a great deal of spiritual weightiness. It would be natural for them to cite his Gospel more sparingly and carefully. That may be a contributing factor to why we do not have documents by the early church fathers which cite John’s Gospel. If they did, they would have done so sparingly, and their use of this Gospel would have been treated with a high degree of respect. Since the New Testament writings were copied and dispersed, but not bound together as one book, they were not conveniently extant (none of these documents were), so the early church fathers would have had to rely on memory in their citations, and this they certainly did.