If theists understood "evidence"

[RoadRunner79]

See above....I think I answer some of your questions.

No, not really.  Paul presumably predates all the Gospels.  I don't see where you went from there as your post didn't make much sense.

I am curious in your support for the claims you made which you make from above though. And what gives you such force to use the highlighted words.

1. )  We can be confident that the work Papias was citing was not the gospel of Matthew that we have today

Because the gospel that Papias refers to was written in Hebrew or Aramaic, not Greek.

2.)  an anonymous gospel which likely drew from earlier sources attributed to Matthew existed by the latter half of the second century

A book without a clear attribution has an unknown or anonymous author.  The text itself doesn't indicate the author and we have only second hand, late attribution of it to Matthew.  The consensus opinion of scholars is that it was anonymous.  As to it likely being dependent upon earlier sources, that seems rather obvious given the tradition, examples of such as in the reuse of Mark and the Thomas Sayings, as well as the fact that its composition is rather late to be the testimony of an eye witness.  Additionally there are textual dependencies between Matthew and the other gospels which indicate that Matthew drew upon other sources.  I don't know why you consider suggesting that something likely drew on earlier sources is using words with force, but whatever.

3. ) There appears strong reason to believe that neither were written by eye witnesses.

Both are rather late for them to be eye witnesses, and, as to the gospel we do have, there is no claim of authorship; both the lateness and lack of authorial attribution argue against the author of the later work being Matthew.  Additionally, it seems rather unlikely that an eye witness would depend upon another source other than himself.  That doesn't fit with the theory that the gospel of Matthew is the product of an eye witness.

I would like to know the reasons for this confidence in these claims.

And I'd like to know if you're doing more than dicking the dog with these questions.  I asked you a question which you don't seem to have answered with anything but some nonsense theory about Paul.

I answered why I thought it was early.... sorry if you didn't understand (I don't see where you think that is "kicking the dog")  You could just say, that you don't understand.  

1.)  Yes there is some dispute about what Papias meant by this.  Was there an earlier Gospel or what.   In any case, Matthew was quoted early in Church History.

2.)   By anonymous, you mean that the author doesn't identify himself within the writing.   However their could have been a cover page, or header which attributes it to Matthew, such as on all the copies that we have these parts do.  I don't think that they just found it along side the road, and decided to put Matthews name on it, so the people who shared the Gospel may have known.   All the information we have points to Matthew as the author, and pretty nothing direct that doesn't.

3.)  You literally used the conclusion in the premise here.  Directly and unmistakably.  Would you care to revise, because this is a text book (over-emphasized) case of begging the question.  Usually it's at least somewhat hidden.  And if an eye witness has heard other's testimony, they will often repeat what they have heard.   In addition, there are many early and recognized Christian creeds within the new testament.   In any case, I hardly see where this is cause for a late dating.   You may note, that this is why detectives separate witnesses as soon as possible before questioning them. 
 
It seems that at most you have a maximum date, where the author was directly attributed to the writing.   Earlier quotes which indicate that the writing was at least partially known before this.  As I was saying before, Paul notes that the gospel (not necessarily this writing, but the story) was early, and as he cautions, and the Early Church demonstrates, they where wary of that which was different from what they where taught.   We don't see any indication of dispute over the writing or the labeling it as Matthew's.   We don't see dispute over it's contents.   It lines up with the Early Church teachings, and the other Gospels.  

Your whole argument seems to be that it late, because it was a late writing, and doesn't really answer the question of why.  Certainly not to use words like "confident"  and "likely" and "strong reason".   As I said, I don't see any reason to doubt those who where closest to the events and shown to be checking for content and authorship, over some conspiracy theory developed 18 centuries later.