In brief, Matthew, Mark and Luke are called the Synoptic Gospels (because they present the same “view” or “synoptic” of Jesus’ ministry) and it has long been noted there is literary dependence amongst them. They copied each other in some way, Dr. Wallace has written a good introductory article on the subject.
Of course, the question immediately followed—who copied whom? Various solutions have been presented. Although a few die-hard adherents hold Luke was the first, the others copied from his Gospel, and even fewer hold to John being first (although not copied by the Synoptic Gospels), the real fight is whether Matthew was first—Matthew Priority—copied by Mark, or Mark was first—Markan Priority—copied by Matthew.
Two primary reasons I cannot be convinced by Matthean Priority, are: 1) harder readings and 2) fatigue.
There is a premise in higher criticism (what this study is generally called) that the Harder reading is the primary reading. The thought behind it being subsequent editors or copiers would modify the reading to make it less difficult. I cannot improve on Dr. Wallace’s statements:
There are several passages in Mark which paint a portrait of Jesus (or the disciples, etc.) that could be misunderstood. These passages have been altered in either Matthew or Luke or both on every occasion. It is the conviction of many NT scholars that this category is a very strong blow to the Griesbach hypothesis—and one which has not been handled adequately by Matthean prioritists.29 Among the several possible passages which scholars have noticed, the following are particularly impressive to me. Still, the cumulative effect is what makes the biggest impression.My First question to Walter Tucker: Why would Mark make the readings harder?
(1) Mark 6:5-6/Matt 13:58—“he could not do any mighty work there except . . . ”/“he did not do many works there . . . because of their unbelief.” On this text Farmer comments: “the passage offers no clear indication that . . . Matthew has ‘toned down’ a phrase in Mark which ‘might cause offense or suggest difficulties’.”30 But this ignores the verbs used, for Mark suggests inability on Jesus’ part, while Matthew simply indicates unwillingness (oujk ejduvnato vs. oujk ejpoivhsen). Cf. also Mark 1:32-34/Matt 8:16/Luke 4:40 for a similar text.
(2) Mark 10:18/Matt 19:17/Luke 18:19—“Good teacher . . . Why do you call me good?” (in Mark and Luke) vs. “Teacher . . . Why do you ask me about what is good?” (Matthew). The text, as Mark has it, might imply that Jesus denies his own deity. It is apparent that Luke did not read it that way, but Matthew probably did. Indeed, in the Holtzmann/Streeter view, Matthew and Luke copied Mark independently of one another. Thus what might offend one would not necessarily offend the other.31
(3) Mark 3:5/Luke 6:10—“he looked around at them with anger/he looked around on them all.” Matthew omits the verse entirely, though he includes material both before and after it (12:12-13). That Luke would omit a statement regarding Jesus’ anger is perfectly understandable.
(4) Mark 1:12/Matt 4:1/Luke 4:1—“the Spirit drove him into the desert” (Mark)/ “Jesus was led into the desert by the Spirit” (Matthew and Luke). Mark uses the very harsh ejkbavllw, while Matthew and Luke use (ajn)avgw, a much gentler term, to describe the Spirit’s role in bringing Jesus to the desert for temptation.
(5) Mark 8:24-26—the different stages of a particular healing story, omitted in Matthew and Luke. The blind man is partially healed the first time by Jesus, then fully the second time. This is the only healing story in the synoptic gospels which required two stages. Perhaps this was the reason for its omission in Matthew/Luke, or perhaps it was the fact that saliva was used as the means of healing.32
(6) Mark 3:20-21—The statement that Jesus’ mother and brothers tried to seize him because they said that he was insane (ejxevsth). Neither Matthew nor Luke have this verse, apparently because it would cast aspersions on Jesus’ mother and brothers.
Here I cannot improve on Mark Goodacre’s article regarding fatigue:
Editorial fatigue is a phenomenon that will inevitably occur when a writer is heavily dependent on another's work. In telling the same story as his predecessor, a writer makes changes in the early stages which he is unable to sustain throughout. Like continuity errors in film and television, examples of fatigue will be unconscious mistakes, small errors of detail which naturally arise in the course of constructing a narrative. They are interesting because they can betray an author's hand, most particularly in revealing to us the identity of his sources.
The clearest way to explain the phenomenon is to illustrate it. Though he did not use the term 'fatigue', G. M. Styler, in his famous article on Marcan priority, draws attention to a strong example, the Death of John the Baptist (Mark 6.14-29 // Matt 14.1-12). (5). For Mark, Herod is always 'king', four times in the passage (vv. 22, 25, 26 and 27). Matthew apparently corrects this to 'tetrarch'. This is a good move: Herod Antipas was not a king but a petty dependent prince and he is called 'tetrarch' by Josephus (Ant. 17. 188; 18. 102, 109, 122) (6). More is the shame, then, that Matthew lapses into calling Herod 'the king' halfway through the story (Matt 14.9), in agreement with Mark (6.26).
Styler points further to a more serious inconsistency in the same verse. The story in Mark is that Herodias wanted to kill John because she had a grudge against him,
'But she could not because Herod feared John, knowing that he was a righteous and holy man, and he protected him. When he heard him, he was greatly perplexed; and yet he liked to listen to him.' (Mark 6.19f).
In Matthew's version of the story, this element has dropped out: now it is Herod and not Herodias who wants him killed (Matt  14.5). When Mark, then, speaks of Herod's 'grief' (perilupoV) at the request for John's head, it is coherent and understandable: Herodias demanded something that Herod did not want. But when Matthew in parallel speaks of the king's grief (kai luphqeiV o basileuV, Matt 14.9), it makes no sense at all. Matthew had told us, after all, that 'Herod wanted to put him to death' (14.5).
The obvious explanation for the inconsistencies of Matthew's account is that he is working from a source. He has made changes in the early stages which he fails to sustain throughout, thus betraying his knowledge of Mark. (7) This is particularly plausible when one notes that Matthew's account is considerably shorter than Mark's: Matthew has overlooked important details in the act of abbreviating. (8) It would be difficult, one would imagine, to forge a convincing argument against this from the perspective of Matthean priority. (9)
Of course the evidence of one pericope alone will not do to establish Marcan priority. It will be helpful, therefore, to turn to Michael Goulder who, in two inspired but brief surveys, draws attention to this 'widespread' phenomenon and lists several examples. (10) One of the most striking is the story of The Cleansing of the Leper (Matt 8.1-4 // Mark 1.40-45 // Luke 5.12-16). (11) Here, just after the Sermon on the Mount (Matt 5-7), Matthew is returning to triple tradition material. He resets the scene by introducing, as often, 'many crowds' (8.1). This soon leads Matthew into difficulties since, like Mark, he has Jesus' injunction to the leper, 'Tell no-one, but go, show yourself to the priest . . . ' (Matt  8.4 // Mark 1.44). As it stands in Matthew this is inexplicable: a miracle that has been witnessed by many crowds is to be kept secret. The parallel in Mark makes it clear how Matthew has become involved in the contradiction: Mark does not have crowds; the leper meets Jesus privately and the command to silence is coherent. That Matthew is involved in docile reproduction here is all the more plausible given the little stress in his Gospel on the secrecy theme that is so prominent a feature of Mark.
We might add a third example that equally points to Matthew's use of Mark, the story of Jesus' Mother and Brothers (Matt 12.46-50 // Mark 3.31-35 // Luke 8.19-21). Here Matthew has returned, once more, to triple tradition material after a section of double tradition material (Matt 12.33-45). The transition between the different kinds of material is smooth, with Matthew's characteristic, 'While he was still speaking to the crowds, behold . . . ' (Matt 12.46). However, the apparent ease of progression from one pericope to the next masks an incongruity, a genuine continuity error in Matthew's account. As in Mark, the mother and the brothers of Jesus are 'standing outside' (eisthkeisan exw, Matt 12.46; Mark 3.31: exw sthkonteV). This makes perfect sense in Mark where Jesus and his disciples are in a house (3.20: kai ercetai eiV oikon) (12) but it makes no sense in Matthew in which no house has been entered and the most recent scene change was a departure from the synagogue, with many following Jesus, in 12.15.
So my second question to Walter Tucker: Fatigue makes sense when looking at Mark --> Matthew. But not Matthew --> Mark. Why would Mark incorrectly refer to Herod as King, if copying from Matthew and he saw “tetrarch”? Doesn’t this infer Matthew (and Luke if one reads the entire article) were copying and demonstrating fatigue?
Thanks, look forward to your responses.