A further reality is that all the Gospels were written anonymously, and none of the writers claims to be an eyewitness. Names are attached to the titles of the Gospels ("the Gospel according to Matthew"), but these titles are later additions to the Gospels, provided by editors and scribes to inform readers who the editors thought were the authorities behind the different versions. That the titles are not original to the Gospels themselves should be clear upon some simple reflection. Whoever wrote Matthew did not call it "The Gospel according to Matthew." The persons who gave it that title are telling you who, in their opinion, wrote it. Authors never title their books "according to."
Moreover, Matthew's Gospel is written completely in the third person, about what "they" — Jesus and the disciples — were doing, never about what "we" — Jesus and the rest of us — were doing. Even when this Gospel narrates the event of Matthew being called to become a disciple, it talks about "him," not about "me." Read the account for yourself (Matthew 9:9). There's not a thing in it that would make you suspect the author is talking about himself.
With John it is even more clear. At the end of the Gospel the author says of the "Beloved Disciple": "This is the disciple who is testifying to these things and has written them, and we know that his testimony is true" (John 21:24). Note how the author differentiates between his source of information, "the disciple who testifies," and himself: "we know that his testimony is true." He/we: this author is not the disciple. He claims to have gotten some of his information from the disciple.
As for the other Gospels, Mark was said to be not a disciple but a companion of Peter, and Luke was a companion of Paul, who also was not a disciple. Even if they had been disciples, it would not guarantee the objectivity or truthfulness of their stories. But in fact none of the writers was an eyewitness, and none of them claims to be.
Who, then, wrote these books?