When I read this, I couldn't think of a reason why there should be a Q, rather than Luke relying on Matthew (or vice versa), but I assumed there had to have been more to the argument. Not knowing what to make of this, this claim has been an open question nagging in my mind.There are serious methodological flaws in the defenses made of the existence and contents of Q, and it looks far more likely to me that what we call ‘Q’ was nothing more than additions made to Mark by Matthew, which were then redacted into Luke. I see no merit in assuming otherwise without very good evidence, and the evidence presented even by staunch advocates of Q cannot honestly be described as even ‘good’. Whereas the evidence for Luke using Matthew is very good (see Chapter 10, §6).
Carrier, Richard. On the Historicity of Jesus: Why We Might Have Reason for Doubt (pp. 309-310). Sheffield Phoenix Press. Kindle Edition.
With that as background, last night I started to listen to last week's episode of Mormonism Live about the historical Jesus, and Bill did an excellent job explaining the Q hypothesis. What you clearly get out of Matthew and Luke is that they both knew that historical Jesus was in fact from Nazareth and they couldn't escape from this well known fact, but they both needed Jesus to be born in Bethlehem to fulfill the prophesy that the Messiah would be born there (Micha 5:2). It turns out that Matthew and Luke both made up completely implausible and completely contradictory stories about how Jesus of Nazareth was really from Bethlehem. If Luke was cribbing off of Matthew, why would he completely change the story of Jesus' birth, which already fulfilled the prophesy about Bethlehem?
Because of this important and material inconsistency (and presumably others like it), it seems more likely that the non-Mark similarities between Matthew and Luke came from "Q".