This sort of objection gets trotted out from time to time: If Matthew was an eyewitness, he would not have used Mark. Therefore, Matthew the Apostle did not write Matthew. Aside from the obvious assumption of Markan priority, which is the most popular theory but by no means certain, there are a number of problems with this objection.
The assumption is that it is unnatural to suppose that for information which Matthew, as one of the Twelve, had already received firsthand he would resort to a book written by Mark, a man who did not even belong to the inner circle of the Twelve.
For starters, the tradition that Mark authored Mark also includes Peter in that Mark is regarded as Peter's stenographer. In that event, Matthew is using Mark, assuming Markan priority, because Mark is, for all intents and purposes, Peter's secretary.
Second, there is some discussion about the young man who ran away at Gethsemane. If this was Mark as a young man, then Mark is an eyewitness of at least part of his own gospel.
Third, if Matthew composed in the Hebrew vernacular and/or, more concretely, in a Jewish / rabbinic style, this would fit with what we have in Acts, in which the Twelve were set apart for teaching, and the first major persecution was against Hellenistic Jews who had become Christians, in which case the Twelve were not among the persecuted. Indeed, Mark could well represent the written core of the teaching of the Twelve about Jesus which they compiled together. It would not be recorded until later, but Matthew had access to it, because the Twelve had gotten their teaching straight, as it were, while together in Jerusalem. Mark is, on this view, the core, Matthew is the extension of the core. Mark, on this view, in its written form comes later than Matthew, because Mark presumably writes it down near Peter's death. Matthew, on this view, comes first, and Matthew, since it borrows from the LXX not the Hebrew text for some OT citations, would be an extended version for the Hellenistic Jewish churches that were planted as a result of the dispersion. One does not need direct literary dependence, e.g. copying from one to the other on such a view, given that memory and verbatim passing down of liturgy was an extremely well developed skill in this society. What we have in Mark is, thus, on this view, the core liturgy. Matthew is a written version of that liturgy with added details from his notes. Matthew's gospel was historically popular for catechumenates to learn for use the more southern geographical areas of the Ante-Nicene church, so this hypothesis fits what we would expect. Should it be objected this is conjecture, the reply would be that Q, Markan priority, and whole host of other theories, especially the idea that communities of Christians composed the gospel involves much more conjecture.
That said, assuming Markan priority, there's a nother problem with the assumption that Matthew would not have used Mark. This assumption is used as a premise in two syllogisms with opposite conclusions:
a. Matthew, eyewitness of Christ's ministry and hearer of his words, wrote the Gospel that bears his name.
b. A close witness, in writing the gospel, would not have felt a need to borrow from or outright use a gospel written by a non-eyewitness.
c. Therefore Matthew did not use Mark.
This one aimed at conservatives evangelicals and sometimes used by them. So, you see, when we discuss this assumption, we are not merely taking aim at critics like Jon Curry. Rather, we are taking aim at those on our own side of the aisle. More on this later.
a. Literary comparison proves "Matthew" depends on Mark for a considerable portion of its contents.
b. A close witness, in composing "Matthew," would not have felt the need to borrow from or use a gospel written by a non-eyewitness.
c. Therefore, the Apostle Matthew, eyewitness of Christ's life and earwitness to His words, cannot have written the gospel, and the tradition that he did so is false.
In both of this the second premise is faulty. For starters, Matthean priority is another live option, so one is just assuming what he must prove in order to hold this in the case of Syllogism 2. The first syllogism is used at times by those asserting Matthean priority. It's a faulty syllogism for them to use, because it assumes a particular order of authorship as well. If one holds to Markan priority already and still uses Syllogism 1, then one would be holding a view that logically pulls away from Markan priority.
More importantly, however:
A. Neither syllogism explains the uniform external attestation to Matthew's authorship.
B. They also do not explain the uniform strong tradition that Mark was Peter's "interpreter."
C. One could, as alluded above one could construct a syllogisthis way:
a. The Apostle Matthew, eyewitness of Christ's deeds and words, wrote the gospel that bears his name.
b. There is uniform tradition that Mark "interpreted" Peter's teaching about Jesus.
c. Matthew mostly likely knew this and esteemed Peter highly, since he was "leader" of the Twelve.
d. Therefore, Matthew enthusiastically used Mark's Gospel. The conclusion that Matthew did not write Matthew if Matthew depends on Mark/because Matthew used Mark is a non-sequitur.
D. The 2nd above syllogism seems to assume that Mark does not reflect Christ's words and deeds accurately. Does it not do that? Does it not do so in a lively way? In order to assert that Matthew would not have used Mark, particularly in Syllogism 2, one is assuming that Mark does not authentically record the events it purports to record. Those who level Syllogism 2 thus tell us more about themselves than they do about the text of Mark. If I was going to write a biography of somebody I knew and somebody else I knew had written one already, and if I considered that a reliable source, why would I not, with his permission even, use that material and then enlarge it, perhaps arrange the material in a particular form for a particular audience to make a particular point? It seems, assuming for the sake of argument Markan priority, that Matthew and Luke would have been more than happy to use Mark, particularly if it was written first.