This is a great post by Matthew Ferguson, the author of the blog Κέλσος and PhD student in Classics. One part I really liked:
First, even if the body of a text does not name its author, there is often still a name and title affixed to a text in our surviving manuscript traditions. These titles normally identify the traditional author. The standard naming convention for ancient works was to place the author’s name in the genitive case (indicating personal possession), followed by the title of the work. Mendell in Tacitus: The Man And His Work notes (pg. 345) that, while not all of our surviving manuscripts are complete with titles, the titles that we do have on some of the best manuscripts traditions have Cor. Taciti Libri (“The Books of Cornelius Tacitus”). This naming convention is important, since it specifically identifies Tacitus as the author of the work. An attribution may still be doubted for any number of reasons, but it is important that there at least be a clear attribution.
Here we already have a problem with the authors of the Gospels. The titles that come down in our manuscript traditions for the Gospels do not even explicitly claim Matthew, Mark, Luke, or John as their authors. Instead, the Gospels have an abnormal title convention, where they instead use the Greek preposition κατά, meaning “according to” or “handed down from,” followed by the traditional names. For example, the Gospel of Matthew is titled εὐαγγέλιον κατὰ Μαθθαίον (“The Gospel according to Matthew”). This is problematic, from the beginning, in that the earliest title traditions already use a grammatical construction to distance themselves from an explicit claim to authorship. Instead, the titles operate more as traditions, where the Gospels have been “handed down” by church traditions affixed to names of figures in the early church, rather than the author being clearly identified. In the case of Tacitus, none of our surviving titles says that the Histories or Annals were written “according to Tacitus” or “handed down from Tacitus.” Instead, we have clear attribution to Tacitus in one case, while only vague and ambivalent attributions in the titles of the Gospels.
I can’t remember where (probably on FRDB), but someone was asking about the weird headings of the Gospels (Κατά Μάρκον::kata Markon, etc.) and asking if this was normal practice in the ancient world. Nope! The titles of the Gospels are in accusative case, not genitive, which he probably meant to say but might have forgotten. Though I did read one argument (again, forgot where) that the first line of Mark’s gospel was probably the title: Ἀρχὴ τοῦ εὐαγγελίου Ἰησοῦ Χριστοῦ, υἱοῦ θεοῦ. Which is indeed in genitive case, but doesn’t actually say that Jesus is the author.
Ferguson has a lot more awesome information about how we know the Gospels were not authored by their traditional namesakes; go read the whole thing! It really expands on one of the sections in my post Why I’m not a Christian.