In the Gospel According to St. John, he frequently uses a term for an apostle who is only called by it throughout the memoir: the beloved disciple, the disciple who Christ loved, or a similar form. Christian Tradition has always held this disciple to be St. John himself, but a definitive explanation for his usage of the phrase has never been given, only many alternatives.
While attending Good Friday Mass, the reading included the account of Christ's Passion as recorded in St. John's Gospel. In it, Christ says to his mother Mary, while indicating the beloved disciple, "Dear woman, here is your son," and to the disciple directly, He said, "here is your mother." (John 19:26-27) By this pronouncement, He was not only putting Mary in St. John's care, and vise versa. The Church has always taught that He was indicating Mary as the mother of all by that designation, not just John. And I believe that John's use of the simple term disciple rather than his own name is textual proof of this.
Why did John substitute beloved disciple for his own name? Everyone who follows Christ, through faith and deed, is His disciple; the apostles were disciples, but Jesus had many disciples other than the apostles, just as many in the Old Testament were Israeli without being the head of one of the Twelve Tribes, and just as a diocese has one bishop but many members. Furthermore, John did not say, "the disciple who Jesus loved especially," or "more than the others"; he simply wrote, "the disciple whom Jesus loved." Well, Christ loves all of His disciples, so giving it that adjective definition was not enough to distinguish the identity of the mysterious disciple - by all appearances.
In fact, I believe that John specifically used not only the generic term "disciple" rather than his own name intentionally, but that he also said "loved" or "beloved", rather than a more qualitative adjective like "most loved", on purpose as well. All Christians are beloved disciples of Christ. God loves all, but by a Christian's voluntary obedience to and love of Christ, sealed by baptism, we become His disciples, and he loves us all equally and completely.
Thus, I believe that St. John used the term "beloved disciple" throughout his Gospel to give a character in the factual narrative that everyone could relate to personally, and also as a model of a good disciple - which the indicated disciple himself, John, certainly was. Now, for all readers of John's Gospel, we have someone to live through vicariously, to put ourselves in the place of and truly live the Gospel.