In my latest reading of Jesus and His Jewish Parables: Rediscovering the Roots of Jesus' Teaching, Brad
 Young critiques the scholarly notion of Markan priority, which states 
that the Gospel of Mark came first, and Matthew and Luke then elaborated
 on Mark. 
If Luke drew from Mark, Young wonders, why does Luke differ from Mark on the order of events?  Why
 does Mark contain things that are absent from Luke and that would have 
coincided with Luke's ideology, such as the story about the 
Syro-Phoenician woman (Mark 7:24-30), which would have fit Luke's 
"emphasis on the role of women (cf. Luke 8:1f.)" (page 136)?  
Why are there times when Mark's story is more elaborate than that of 
Luke, such as the story of the healing of the epileptic child (Mark 
9:14-29; Luke 9:37-43)?  Why are there times when Matthew and Luke agree
 on a story while disagreeing with Mark?  For Young, one could argue that Mark came after Luke in date.
But, if that were the case, why would Mark omit so many things that are in Luke? 
 According to Young, Mark is communicating to a Hellenistic society.  
His Gospel focuses on Jesus' activity----things occurring immediately, 
Jesus moving rapidly, crowds following him, etc.  Young states 
on page 138 that "The instruction of Jesus would probably be less 
important to a non-Jewish, pagan audience", and that "the miracles and 
activities of Jesus would be considered a better vehicle of 
communication."  Young goes on to say that we don't really know
 why Mark would omit things, but Young does see parallels between Mark 
and Hellenistic miracle stories.  Mark presents Jesus using 
"thaumaturgic healing techniques", which "have their parallels in 
Hellenistic miracle stories where spittle was employed by the miracle 
worker and one finds another story where the blind man first sees trees 
after being healed (Mark 7:32-37; 8:22-26)" (page 139).  I think
 that a pagan audience would have been open to reading about Jesus' 
teachings, for pagans had their own teachers.  At the same time, I can 
see the point in a Gospel that focused on Jesus' activity. 
The
 scenario that Young appears to prefer is one in which Matthew and Luke 
use a common source (though there are times when Luke draws instead from
 a reconstruction of that source), which accounts for when Matthew and 
Luke agree with each other and disagree with Mark.  Young thinks that Matthew used Mark, but that Mark came after Luke. 
I thought of Mark Goodacre's The Case Against Q as I read Young's discussion.  Goodacre
 favors Markan priority, but he makes similar arguments to those of 
Young, only for different ends.  Goodacre asks, for example, why Mark 
would omit the Lord's Prayer if the Gospel of Mark came after Luke and 
Matthew in date, since the Lord's prayer has themes that coincide with 
Markan ideas, plus Mark is big on prayer.  For Goodacre, that indicates the greater likelihood that Matthew and Luke came after Mark than vice versa.  This
 resembles Young's argument that Luke came before Mark in date, for 
Young wonders why Luke would omit things Mark has that coincide with 
Luke's message, if Luke were using Mark as a source. 
Goodacre
 also seeks to explain why Luke would omit or rearrange things.  
Goodacre states that Luke does so for his own ideological and literary 
purposes.  Goodacre also notes that movies about Jesus omit or 
rearrange things from the Gospels, yet these movies are obviously aware 
of the Gospels, so Luke could have omitted and rearranged things from 
Mark (and also Matthew, for Goodacre thinks that Luke drew from Matthew 
rather than Q) while being aware of those sources.  This resembles 
Young's argument that Mark omitted details from Luke for his own 
agenda.