Why should I believe that?
Most of the epistles written by one of Jesus 12 disciples are disputed, meaning that scholars debate who their actual authors are. For example, 1 Peter and 2 Peter have stylistic differences, meaning they have two different authors. This means that at least one, and perhaps both, were not written by Peter. James, Jude, and the 3 epistles of John are all disputed as to who wrote them. Remember that at that time, it was considered perfectly normal to write a text and attribute it to some significant person -- it was not considered lying in that culture. Now let's talk about the gospels.
When the gospels were first completed and passed around among the churches, they were ANONYMOUS. It was only later in the early second century (or late first century in the earliest) that the tradition was formed that they were written by Matthew, Mark, Luke and John. IOW it was just a nice idea that had no foundation.
We know from textual analysis that each of the gospels were written by more than one author, and their works spliced together. For example, the original text of John was what scholars call the Signs Gospel, which was later added to by one or possibly two other authors.
This multiple author thing, late editing, and hostility towards Jews tends to indicate that they were not written by religious Judeans like Matthew or John, but by either Hellenized Jews from the diaspora or perhaps Gentiles. In any case, NOT eye witnesses.
Now, we all have our opinions, so if you want to stick with "They were written by Matthew, et al" I understand.