What are your reasons for believing that Matthew the Tax Collector (or Matthias, the apostle chosen in Judas' place) didn't write the gospel attributed to him?
Because they didn't have a clue about the real Galilean man who existed.
Had these been the real followers we would not see as much rhetorical prose and layered mythology on top of what has possibilities of actually taken place.
Example. Earliest Mark is almost silent on the resurrection. Because in marks time the resurrection was not that important and the theology was still growing. BY L and M time, the theology had expanded in detailed legends, the issue is we see exactly who they paralleled in rhetoric and we see each's theological motives that also represent later dates. Basically we see them expanding on Mark, NO eyewitness would do that.
Example. The birth legends are stated to be fiction by credible historians, they also contradict each other in many details which are also layered over Marks foundation. Scholars view both of these communities NOT "people" as far removed from any actual event. Their theology represents Hellenistic Proselytes and gentiles over that of Aramaic Judaism.
Many areas show ignorance of Aramaic Judaism, and none of the traditions are from an early enough source that had the true Aramaic teachings. There are very few Aramaic transliterations in all of the NT. So these communities were far removed from any actual event in the life of the man.
On the surface, this has been taken to imply that Matthew's Gospel itself was written in Hebrew or Aramaic by the apostle Matthew and later translated into Greek,
but nowhere does the author claim to have been an eyewitness to events, and Matthew's Greek "reveals none of the telltale marks of a translation."
[17][14] Scholars have put forward several theories to explain Papias: perhaps Matthew wrote two gospels, one, now lost, in Hebrew, the other our Greek version; or perhaps the
logia was a collection of sayings rather than the gospel; or by
dialektōi Papias may have meant that Matthew wrote in the Jewish style rather than in the Hebrew language.
[16] The consensus is that Papias does not describe the Gospel of Matthew as we know it, and it is generally accepted that Matthew was written in Greek, not Aramaic or Hebrew
This is pretty important if he actually followed the man around in person, he surely would have noted it.