If one takes a course in Intro to the NT, one might be told with great confidence that the Gospel of Matthew was written in Antioch. This has become received wisdom in the discipline. It's also built upon a remarkably shaky foundation. As best I can tell, it was B.F. Streeter who really popularized this view. Streeter's reasoning goes much like this: the canonical gospels were all written in major Christian centres; all major centres but Antioch are ruled out by process of elimination; therefore, it must have originated in Antioch. He goes on to present a historical narrative in which refugees from the Jerusalem church fled to Antioch in 66 with what source critics like to call "M," i.e. the material distinct to Matthew's Gospel. Here he commits a strange move: his argument for why Matthew's Gospel cannot have been written in Palestine is that the distinctly Matthean material is generally "inauthentic"; leaving aside the questionable judgment about authenticity and the idea that it rules out a Palestinian provenance, the argument that precisely those parts of Matthew's Gospel that originated in Palestine rule out Palestine seems passing strange. This strangeness should alert us that something peculiar is happening off-stage.
That something seems to be the data. It seems that Streeter cannot deny that there is good reason to associate Matthew's Gospel with Palestine, yet is somewhat at a lost to explain why it cannot have been written in Palestine itself. For instance, he knows that the data strongly points towards Palestine. In fact, Papias's account of the origins of Matthew's Gospel is what allows him to rule out Rome and Asia Minor as the place of composition: his reasoning is that, at the very least, it shows that Matthew's Gospel originated in the east. He knows that the text is attributed to a prominent figure associated with the Jerusalem church, and that even if we judge that the attribution is false the fact it is to this figure, and only this figure, remains probative; Streeter must simply dismiss the data of the attribution. He knows that this is the most "Jewish" of gospels (that's why he rules out Alexandria). He is aware of the alliances between Matthew's Gospel and the Didache and the epistle of James, both of which are also attributed to leaders of the Jerusalem church. He knows that the data all tends in the direction of a Jerusalem provenance. Yet it seems that his broader historical narrative blocks him from making that judgment.
I would suggest that the real reason for this blockage is to be found in his discussion about the refugees who fled from Jerusalem to Antioch in 66: Streeter cannot locate Matthew's Gospel in Jerusalem because he has already judged it to be the case that as of 66 Jerusalem was no longer a major Christian centre. As such, it does not satisfy his conditions as a place of composition for Matthew's gospel. Now, I am prepared to concede that the gospels likely were written for the most part in major Christian centres, but not for the reasons that Streeter gives (namely, that these anonymous texts required the authority of a major centre to achieve acceptance). My own thinking is that only major Christian centres had the material resources necessary to produce such texts. Dashing off a letter here or there is one thing, but a large narrative text that would have likely been copied at least one prior to circulation; this to me seems to suggest something more in terms of communal infrastructure. Given the evidence suggesting that the Jerusalem church relocated to Pella in 66, I don't see how we can rule out that much of this infrastructure was reconstructed there. Moreover, if Pella was understood as a sort of Jerusalem-church-in-exile, then it's entirely possible that even on Streeter's own terms this would have been, however briefly, a major Christian centre. Not to mention, it's not like the Jerusalem church never rebuilt itself. The same sources that tell us that they fled in 66 also tell us that they returned, and that there was a Jewish-Christian community in Jerusalem at least as late as c. 132. And this doesn't even begin to touch the obvious question: what if Matthew's Gospel was written before 66?
When we get into it, Streeter's argument for the Antiochene origin of Matthew's Gospel is really based upon arguments from what he supposes must have been the case, and then a process of elimination by which he excludes any possibility that does not fit with that supposition. Positive evidence is almost entirely lacking (some possible quotations in Ignatius, the similarity with the Didache, neither of which seem particularly strong to establish the place of composition: Ignatius, because it's not like he couldn't have quoted material that didn't originate in Antioch, and the Didache because the argument that it is of Syrian provenance is itself quite weak). It represents the triumph of antecedent supposition. Rather than allowing the data to serve as a corrective to his supposition, he has allowed his supposition to serve as corrective to the data.