To what degree does the Didache depend on Matthew or vise versa?

Question

Reading the Didache for the first time, I was struck by many similarities between it and Matthew (particularly the Sermon on the Mount section). For instance, this is from the first chapter of the Didache:

If someone strikes your right cheek, turn to him the other also, and you shall be perfect. If someone impresses you for one mile, go with him two. If someone takes your cloak, give him also your coat. If someone takes from you what is yours, ask it not back, for indeed you are not able.—Didache 1:10-13 (Roberts-Donaldson)

And this is from Matthew:

“You have heard that it was said, ‘An eye for an eye and a tooth for a tooth.’ But I say to you, Do not resist the one who is evil. But if anyone slaps you on the right cheek, turn to him the other also. And if anyone would sue you and take your tunic, let him have your cloak as well. And if anyone forces you to go one mile, go with him two miles.  Give to the one who begs from you, and do not refuse the one who would borrow from you.—Matthew 5:38-42 (ESV)

According to Wikipedia:

In modern scholarship a new consensus is emerging which dates the Didache at about the turn of the 2nd Century. At the same time, significant similarities between the Didache and the gospel of Matthew have been found as these writings share words, phrases, and motifs. There is also an increasing reluctance of modern scholars to support the thesis that the Didache used Matthew.

On what basis do scholars reject the dependence of the Didache on Matthew? If there is no dependence, where would the seemingly common teachings have originated? (Note that Wikipedia provides no references for this particular claim.)

Answer 1

My impression is not that there's good evidence to reject direct dependence of the Didache on Matthew, but rather that the evidence of direct dependence has been called into doubt. There just doesn't seem to be a smoking gun that can show that the Didache is literally copying from a written version of Matthew. Here's one article arguing against dependence, so you can see the sort of arguments that come up. An example suggesting the lack of acceptance of dependence, but not providing an argument, is "Reconstructing the social and religious milieu of the Didache: observations and possible results" where Zangenberg states "In terms of contents, the only manifest connection between Didache and New Testament writings concerns the Synoptic tradition, first and foremost Matthew, but nowhere is it necessary to assume a direct literary dependence."

Furthermore, many scholars think that Matthew and the Didache came from roughly the same community (Syria, though Matthew probably from a city and the Didache from a rural area). This suggests all sorts of other possible relationships. For example, it may be that Matthew and the Didache are drawing on the same oral traditions in the same community. Or perhaps the Sermon on the Mount was being circulated in that community before later being edited and incorporated into Matthew. Or maybe there was an early version of parts of the Didache which influenced the author of Matthew, but the final editor of the Didache did know Matthew. Which is not to say that there's conclusive evidence for any of these options either, just that it's difficult to be certain what the exact nature of the close relationship is. There's several books about what this community may have been like and how that is reflected in the Didache and Matthew (and possibly James), see the collections Matthew and the Didache and Matthew, James, and the Didache.

To summarize, my understanding is that there's not a clear scholarly consensus on the exact relationship between Matthew and the Didache (e.g. earlychristianwritings reports no such consensus). Probably what wikipedia means is that the older consensus of direct literary dependence is breaking down, not that there's a new consensus against direct literary dependence. I wish I had better evidence to back this up (I did look into this in more detail at one point), but ultimately it's a bit hard to provide quick evidence of a non-existence of consensus because of course each individual scholar has their own opinions.