(I originally and briefly included this in my "what's doing" post nearby, but thought it might be better as a stand-alone post.)
One of the prevailing views of the first three Gospels is that even if a single human author brought each Gospel text together, he relied on at least two, pre-existing, written sources, from which he took existing text and inserted into his Gospel. This conclusion is reached by noting the similarities of large sections of Matthew, Mark and Luke, and yet there are similarities between two but not three, suggesting a source other than Mark--the presumptive source of what is common in all three.
I am not in a position to dispute with scholars on this point. However, one expectation growing out of this consensus theory is that the Gospel texts will be "uneven"--i.e., at various points, you can see the "seams" where the author/editor "stitched" things together. If you have a Catholic Bible with extensive notes, such as the New American Bible, or the Catholic Study Bible, you will see this reflected in the notes: "here the author inserts text from 'Q'" (the suppositional second source-document for Matthew and Luke), or words to that effect.
Well, in the seminary, Father Tim Schehr -- not commenting directly on this theory of the Gospels -- recommended something interesting: try reading the text as a unity. Sometimes surprising things come to light.
In the case of the Gospel of Matthew, thus far--we are about midway in chapter 8 -- the unity of the text seems very strong. Many treat the section dubbed the "Sermon on the Mount" (realize this way of sub-dividing the text does not come from Matthew--he writes a continuous narrative) as a grab-bag of various teachings and sayings by the Lord, inserted by Matthew here. But a funny thing happened as we simply read it: it seems to have very clear themes running throughout the "sermon," and indeed, the section immediately after seems to launch from content of the sermon.
Near the end of the "sermon," our Lord warns about who are true disciples, and who are not, and he says, "not everyone who says, 'Lord, Lord,'" will be well received; he will say, "depart from me." Recall that the entire sermon was given in the hearing of the crowds, but with the disciples front-and-center. Then he comes down the mountain, and right away, someone approaches him, and calls him...Lord. It is the first time anyone calls him that. It is a leper. Our Lord's response indicates, he is a true disciple: he is well received. Then, someone else approaches, and calls him Lord, twice -- it is the centurion, a pagan Roman! He is presented, if possible, even more favorably, as a model of faith, than the leper. After this, the Lord arrives at Peter's house, and there finds Peter's mother-in-law sick. The Lord heals her.
But note: no appeal from Peter to come and heal; none of the disciples gathered around the Lord have yet to call him Lord! They are silent: they are observing and learning. We don't know if Peter even knew his mother-in-law was sick, but if he did, his inaction compares unfavorably with the centurion, who said, "I am not worthy that you should enter under my roof"--and it's not even necessary--just say the word.
One of the facile things people say about the Gospel of Matthew is that is so Jewish. Well, it is Jewish, but so are all the Gospels, Luke to a lesser degree, but still. What they go on to suggest is that it reflects an exclusive mindset: you have to be Jewish to be Jesus' disciple. And the indications I've just cited, along with many others, show the flaw of that idea.
Not only does Matthew show the first two people to be received as disciples to be outsiders--a leper and a pagan Roman--the latter is praised by the Lord as showing greater faith than any in Israel--and on that occasion, we hear many will come from east and west (in context, meaning Gentiles), to recline with Abraham, while "the children" (i.e., some of them) will be cast out. Also, remember the opening genealogy of Matthew, a text many simply ignore. But you will find Matthew highlights several people in the list who are outcasts -- a prostitute and someone involved in incest -- but two people who are non-Jews: the aforenamed prostitute, Rahab, but also Ruth.
And recall the story of the Magi, told only by Matthew: Gentile star-gazers are more open to Jesus and come seeking him to worship, while the Jewish religious and political leadership only a few miles away, either misses it, or is uninterested (note even after the Magi visit, the scholars do not come to Bethlehem to investigate), or come, in Herod's case, to kill.