Craig A. Evans, “The Two Source Hypothesis,” in The Synoptic Problem: Four Views, edited by Stanley E. Porter and Bryan R. Dyer (Baker Academic, 2016), 34-35.
Matthew and Luke make good exegetical sense as interpretations and adaptations of Mark, but Mark makes little sense as an interpretation and conflation of Matthew and Luke. When compared to Mark, Matthew’s interest in showing how Jesus fulfills both prophecy and law is plainly evidence. When compared to Mark, Luke’s interest in showing how Jesus’s saving work applies to the marginalized, including Gentiles, is hard to miss. Countless commentaries and scholarly monographs have benefited from the recognition of Markan priority and the respective ways the evangelists Matthew and Luke have made use of the earlier Gospel.
This cannot be said for the hypothesis that views Mark as the last to be written and as drawing on the Gospels of Matthew and Luke. No one has written a detailed commentary that shows how our understanding of Mark is enhanced by seeing how he has blended or omitted Matthean and Lukan materials. Matthew prioritists speak of Peter, the voice behind Mark, as attempting to bring together the divergent Jewish and Hellenistic views of Matthew and Luke respectively. This is plausible in theory, but there has been no success in showing how exegetically this is actually so. One would think, moreover, that the tradition of authentic Petrine material lying behind Mark fits better with an early Mark, on which later evangelists would rely.
The Amateur Exegete 
Thanks for posting this.
While I have seen occasional attempts to promote Matthean priority on the internet and in older scholarly works, I try to take them with a grain of salt for several reasons (including those given above and the idea of editorial fatigue).
Evans’ discussion of Petrine source material didn’t surprise me too much (given his mostly conservative approach to scholarship) but it still seems difficult to believe that Peter would have failed to tell Mark about Jesus granting him apostolic authority as “the rock on which the church would be built” (found in Matthew). There’s also the tendency of the latter (and Luke) to “correct” Mark on information about Jewish customs and scriptural citations, which doesn’t fit too well with the original source being a prominent disciple listening to the actual words of Jesus.
Perhaps the strongest attempt to defend a Petrine source behind Mark is the notion that several potentially embarrassing anecdotes about Peter are omitted there but included in the later synoptics. However, this doesn’t explain the omission of the “rock of the church” pericope above or why Mark still decided to include Peter’s denial of Jesus. (Let alone the reconciliation of Peter to Jesus found in John and implied in the post-resurrection stories of the other synoptics.)
Apologies if it sounds like I am preaching to the choir.
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Also, as the history of post-canonical gospels (and apostolic acts) shows, the general tendency is toward additional expansiveness, another reason to reject the two-gospel theory, as Mark doesn’t do that.
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