Why Matthew, Mark, Luke?

Let's take a look at the claimed authorship of the three Synoptic Gospels - Matthew, Mark, and Luke. Now, one must remember that these three books had an enormous impact within the early Christian movement in the late first and early second centuries. Papias and Irenaeus in the early and late second century wrote of their testimony that the authors are who we think they are today. Currently, the vast majority of scholars agree that there are no known credible competitors to the authorship of those three books. But let's examine who these authors were.

Two of the three weren't even members of the original twelve apostles (Mark and Luke). The one author that was an apostle (Matthew) was probably one of the most despised persons among the Jews of his day since, before becoming a follower of Jesus, Matthew was a tax collector. Tax collectors were loathed and were generally outcasts from Jewish society.

If we are to believe these three books of the New Testament were “made up” and not historically accurate, why would the fabricator attach names like these to those books? If the gospels were fabricated but still wanted to be as authoritative as possible, surely other names would have been more appropriate, like Peter for example. In fact, to prove the point, we do find writings that appear generations later attached with just the names you would guess would be used to add more gravitas and respectability - Peter, Mary, James, and Philip (i.e. the Nag Hammadi library which is dated probably in the 200s AD and which many scholars consider false writings). Among the Christian community, these names carried more weight than non-disciples such as Mark and Luke.

One can conclude that these books were attributed to people like Matthew, Mark and Luke because that is who truly wrote them, and because the quest for truth and accuracy was of paramount concern.

References:
Strobel, Lee, "The Case for Christ"
Geisler, Norman L., "I Don't Have Enough Faith To Be An Atheist"