The first question posed is: Was the Beloved Disciple the author of the Fourth Gospel?
This explicit claim of authorship in verse 24 of the last chapter of the fourth gospel, "This is the disciple which testifieth of these things, and wrote these things". Moreover, it is clear "the disciple" refers to the one identified as "the disciple whom Jesus loved" in verse 20 and elsewhere in the gospel (starting with the first mention of this unnamed disciple at the last supper, which is also reconfirmed here in verse 20).
So those who are willing to rely on the authority of God's word (instead of trusting in non-Bible sources and the traditions of men) will let the plain text of scripture answer that question. Yes, the author of the fourth gospel was the beloved disciple.
Then there is a subsequent question asking how those "who reject John Zebedee as the author of the Fourth Gospel reconcile this passage"?
And that answer is also made evident by the text of scripture itself. Two things are true: (A) there not a single verse that would justify teaching that John was the unnamed "disciple whom Jesus loved" and (B) the facts recorded in scripture prove WHOEVER the beloved disciple was he could not have been John.
There are facts recorded about John that are mutually exclusive with facts that the author of the fourth gospel tells us about himself. Of course, there is no problem with scripture. Rather this problem only occurs when one tries to force the unbiblical John tradition on the text, in spite of the biblical evidence to the contrary. So the false tradition that has taught people to ignore the biblical evidence and follow after non-Bible sources who claim this unnamed author was John is the cause of the problem.
Therefore, there is nothing to reconcile (as far as John Zebedee is concerned) when it comes to the claim of authorship that was recorded by the "disciple whom Jesus loved" in the closing words of his gospel, because this unnamed author was not John.
A comment claims verses 20-24 offer "the best evidence against John", but the truth is the entire body of biblical evidence on the one whom "Jesus loved" (who is only mentioned in the fourth gospel) stands in stark contrast to all of the facts recorded in scripture about John, including the fact that every event where John is mentioned in the first three gospels is missing from the fourth gospel. [Edit in reponse to comment: FYI "every event where John is mentioned in the first three gospels is missing from the fourth gospel" does not say "every event where the disciples are mentioned…", and it could not possibly mean that, since clearly there are such events noted in the fourth gospel that are also in the first three gospels. Therefore, the words "where John is mentioned" were obviously not intended to exclude events where the "disciples", "apostles" or "the twelve" are mentioned but, rather, the phrase "where John is mentioned" means just what it says, i.e. where "John" is mentioned (in other words where those writers took time to actually refer to John in particular -- where they mentioned him by name).]
TheDiscipleWhomJesusLoved.com has a free eBook that presents the biblical evidence that can prove the beloved disciple was not John (including the mutually exclusive facts noted above) and those who care to weigh the biblical evidence on this topic may find this resource helpful as they seek the guidance of scripture when it comes to answering questions about the anonymous author of the fourth gospel.
-- edit in response to comment:
Regarding the statement: I see a discrepancy between your statement that we should not trust in non-Biblical sources, and your claim that the answer can be found in an eBook.
It's really not that difficult to grasp, provided one is willing to admit and is able to understanding that there is a difference between the message and the messenger. The telegram that was received by a man in a prior generation received that ordered him to "report for duty" was not founded on authority of the delivery boy or one who typed the message. Rather, it was founded on the authority of the source.
The authority of God's word is not dependent on whether it is heard quoted from the pulpit, read in the Bible, communicated in sign-language or printed in a tract. Likewise, in discussing topics in God's word, if an eBook, a lay person, a radio preacher, or a bum on the street has accurately represented God's word on a given point, it would surely be a foolish mistake to think the truth found in God's word can be ignored simply because one does not like the messenger or the format used to communicate that truth.
That said, those who carefully read my post will notice it says the free eBook is a presentation of the BIBLICAL EVIDENCE that proves John was not the beloved disciple who wrote the fourth gospel. Since scripture is the only source cited in the book, it is the testimony of the inspired writers of scripture that the readers of the eBook are asked to respect. The biblical evidence presented in the book either does or does not prove the case. But that case is not dependent on the authority of the eBook.
Laying out a case based SOLELY on citing the facts found the plain text of scripture is just the opposite of method of asking people to trust in this-or-that non-Bible source, which is the technique that is used to sell people on man-made traditions like the John idea. As noted above, there is not a single verse that would justify teaching the John idea and that is why the idea starts with a non-Bible source that claims John was the beloved disciple and then proceeds to use circular reasoning to assert that all the passages that mention the unnamed "other disciple, whom Jesus loved" are talking about John. Usually the sales pitch includes the claim that 'John called himself the disciple whom Jesus loved in order to be humble' - a silly notion indeed, given that writers like Paul in his letters and John in the Book of Revelation were inspired to repeatedly identify themselves by their own name and it would be ridiculous to think their doing so was a prideful act.
(Thank you, Jack.)
-- edit in response to comment:
With any body of evidence that is presented for consideration, some people may conclude that evidence does prove 'x' and others who are offered that same evidence people will say it does not do so. As the OJ jury exemplified, evidence is not weighed in a vacuum. The verdict of those who purport to weigh the evidence in a given instance is shaped by the prejudices and assumptions they bring to the table. Many people believe unbiblical traditions and their allegiance to tradition shapes their view of scripture.
Likewise, those wedded to the John tradition will ignore the fact there is not a single verse that justifies teaching the John idea and they can find an excuse to turn-a-blind-eye to the facts in the biblical record that argue against that idea. One can discount this-or-that fact in the case against the John tradition and pretend that means all other biblical evidence against the John idea can be ignored. So be it.
The biblical evidence is available for all Bible students to see and evaluate for themselves and the words of scripture will persuade those who have a love of the truth. So I will continue to urge others to respect the authority of God's word and encourage them to "prove all things", this issue included. And to those who choose to see things differently, it would seem good to leave it with the words that we see used in scripture by those who found themselves in disagreement: "The Lord judge between me and thee".