If theists understood "evidence"

[Angrboda]

The Gospel of Peter was likely written "late", but then, again, so was Matthew:

Early Christian Writings

Neither are serious historical accounts of the life of Jesus.

Why do you think that it was written late?  What is your evidence or reasons?   A few of the NT documents did have some dispute over whether they should be included; but, I don't think that Matthew was one of them.  It seems that the early Church believed that it was Matthew the very same disciple who founded some of those Churches.  We also see the same accounts quoted early in the Church, and being used for teaching.   

https://bible.org/seriespage/matthew-int...nd-outline

In the first place, the late dating of the Gospel of Peter seems to be based on nothing more than speculation. If you have reason to think otherwise, please present it. Ignoring the internal evidence, which doesn't really lead us to Matthew, the article you quote implies that the gospel of Matthew was written by the same author as that of the work Papias cites solely by virtue of the fact that the gospel of Matthew was later attributed to Matthew. It gives no other justification for the assumption. We can be confident that the work Papias was citing was not the gospel of Matthew that we have today, and it's unclear whether Ignatius is alluding to events in the work that Papias is referencing, or to the gospel of Matthew that we have today; it could be either. So the best we can say is that there is evidence to indicate that a work attributed to Matthew existed by the first half of the second century, and an anonymous gospel which likely drew from earlier sources attributed to Matthew existed by the latter half of the second century. According to Wikipedia, the gospel of Peter is also believed to date to the first half of the second century. There appears strong reason to believe that neither were written by eye witnesses. How any of this shows that the gospel of Matthew should be privileged above the gospel of Peter is a mystery to me (and doctrinal positions don't count as that argument leads nowhere). So what exactly are you basing your preference for Matthew over Peter upon?