I had a question brought to me today that I found quite intriguing. Here is my best attempt at a plausible answer.
Mark 2:16-33 tells the story of Herod the Great ordering the slaughtering of every male under 2-years-old in the city of Bethlehem in an attempt to kill the "new king." The question was, "Why doesn't Luke include this material?"
I believe the reason why Luke may not include this story is that Luke is primarily concerned with declarations of who Jesus is. These things fill the Lukan birth narrative (Luke 1-2). These declarations were meant to establish the authority and credibility of Jesus to Luke's Gentile readers.
So, why would Matthew include this story? Matthew is writing to a Jewish audience, who would recognize the emotions felt by Herod (jealousy) and the significance of Bethlehem (the ancestral city of the great King David). Luke's Gentile audience may not know these things.
Even if we consider Luke as a neutral historian, the account of the slaughtering of all males under the age of 2 in a tiny village would be of inconsequential significance to the history of this new Christian movement.
Additionally, one may ask why neither Mark nor John includes this story. They have no birth narratives at all, so the absence of this section seems trivial.