This is a quote from Raymond Brown found here in this debate. I wanted to respond to it (my words in red).
As explained in Chapter 6, This INTRODUCTION works with the thesis that Matt and Luke used Mark. Yet for many centuries the dominant view was Augustine's thesis that Mark was little more than an epitome of Matt; and recently attention has been given to the (modified) Griesbach hypothesis wherein Mark drew on Matt (p. 113 above). It is instructive to test the theological consequences of positing Marcan dependence on the other Synoptics. For instance, Mark would have omitted the Lord's Prayer and the four beatitudes that Matt and Luke agree upon.At a first glance, most of the Marcan priority arguments seem to hold water. However, on further inspection, they all seem to be as theologically motivated as their supporters often accuse the gospels themselves of being. They fundamentally assume that the gospels do not record real history (if so, only loosely) – variations must be explained by theological agendas. Out right they deny inspiration – which is the goal of historical critical examination I suppose, but at least one option must be that what they say is actually true.
And John omits Christ raising the Synagogue ruler's daughter from the dead (whereas John himself was one of only three present when it happened) and the virgin birth. You can see how unhelpful this sort of reasoning is for Christians.
As for christology, if Mark was written after Matt and drew on it, at a period when the title "God" for Jesus was becoming more common, Mark 10:17-18 would have complicated Matt 19:16-17 by gratuitously introducing an objection to giving Jesus a title that belonged to God alone.
The implication present in Matthew is strong enough to shrug this point off. It’s also quite conceivable (not to scholars like Brown of course) that Peter, or Mark by interpretation is recalling wording which closer replicates what was actually said at the time. If Jesus’ words were spoken verbatim as recorded by Mark, that would make complete sense of the whole issue and would not contradict Matthew in the least.
What Brown and scholars like him never comprehend is that it IS actually possible that the gospel writers sincerely believed what they wrote to be true and weren’t fabricating details for theological purposes. Since they rule out honesty a priori, they often come up with some pretty ridiculous theories.
Mark 6:5 would have introduced the idea that Jesus could not do miracles at Nazareth, changing the statement of Matt 13:58 that he did none.
First of all, if you have any point, it’s that Matthew corrected Mark… it wasn’t that he couldn’t do miracles it was that he just didn’t – this is incompatible with belief in the inspiration of Scriptures. Secondly, I don’t know of the usage here and the linguistic argument but we often use the word “couldn’t” in non-literal ways ourselves. It wouldn’t take much to convince me that they could have done the same. “I couldn’t bring myself to look”. Well literally you could have if you wanted to.. You just didn’t want to. “I couldn’t help him with that he was being a complete jerk”. In reality, you could have helped you just didn’t because he was a jerk. “Jesus couldn’t do any miracles because of their lack of faith”. In reality, He could have regardless of which gospel came first – He just didn’t and Mark’s gospel saying the latter may have been part of a colloquial expression or happenstance as Peter recited the incident. It may have been particular to Peter’s way of talking. In short, there’s a host of reasons why this could have happened without assuming Marcan priority.
"Some claim that Matthean priority and Marcan dependence support traditional Roman Catholic positions,
It does. Have you heard of a group of guys called the early Church fathers?
but Mark's presentation of Mary and Peter becomes all the more difficult if the evangelist knew Matt and/or Luke. Mark would have deliberately omitted the infancy narratives of Matt and Luke, even the details in which they both agree, including the conception of Jesus through the Holy Spirit.
So did John’s what’s your point? If it proves anything at all it proves too much. If this were evidence of Marcan priority it would be evidence for Johanine priority as well. If it proved that Mark was unaware of these facts (assuming Matthean priority) it proves John was as well (or if you’re willing to go that far I’m sure you’re willing deny Johanine authorship – we still have problems with this of course).
Mark would have consciously added two items lacking in Matt and Luke pertinent to Mary, namely, that Jesus' own family thought he was "beside himself" (3:19b-21) and that he received no honor from his own relatives (6:4).
Again, are we to rule out the possibility that these things actually happened a priori? If we assume that the gospels were only loosely based on history and mostly theologically charged, this point makes sense. But if we were to consider the possibility that, His family really was beside themselves at one time or that He really did receive no honor from his family at one point, then it makes perfect sense that Mark would have added it.
As for the Marcan view of Peter and the apostles, Mark would have deliberately omitted both Matt 16:16-19 that makes Peter the rock on which the church was built, and Luke 22:31-34 that has Peter strengthening his brothers after his own failure. (Even though those are not passages shared by both Matt and Luke, Mark can scarcely not have noticed the impact of omitting such positive passages.)
There are many things omitted in regards to saint Peter in Mark. It’s striking actually – especially when Peter is said to have delivered this gospel as a homily based on Matthew and Mark reconciled the shorthand notes with Matthew & Luke adding nothing and taking nothing away. Peter doesn’t walk on the water in Mark, several comments and actions made by anonymous disciples are actually from Peter (including the one who drew his sword and cut off the ear of the high priests’ servant).
But again, this kind of reasoning doesn’t get us far (at least not in the right direction). John shows that Andrew was called first, not Peter. Why, if the gospel authors were so theologically motivated would John not fabricate that Peter was called first since that would make the most sense and seems to be what the Synoptics imply.
Of course, Peter may have omitted the details out of humility. Why Mark didn’t reconcile it with Matthew may be a mystery, but no more of a mystery (in fact much less) that John – while attempting to prove the divinity of Christ omitted the virgin birth.
Mark would have deliberately omitted the promise of Jesus to the disciples in Matt 19:28 and Luke 22:29-30 whereby they would sit on thrones judging the twelve tribes of Israel.
If Mark was written primarily to Gentiles in Rome would this be so difficult to imagine him doing?
Mark 4:38 would have made the disciples more rude to Jesus than they were in Matt 8:25.
With 12 disciples, there were doubtlessly several types of reactions and Mark giving it from one perspective while Matthew giving it from another neither proves nor even suggests anything at all.
Using a book with the Gospels in parallel columns, readers are invited to test other examples of Marcan thought and procedure in the Griesbach hypothesis."
If I had no other reasons, I think I would believe in Marcan priority but since the early Church fathers unanimously affirm Matthean Priority (plus the existence of his gospel in Hebrew/Aramaic up until the 5th century) and since Matthean priority can be soundly defended, I am going to stick with the early Church on this one. Now I know Pope Benedict believes in Marcan priority along with most scholars but there are good scholars (Scott Hahn for one) who believe in Matthean priority.