Fuel, here’s the issue as I understand it, with regard to “Q” and textual criticism of the Gospels in general:
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Matthew composes a gospel whose primary purpose is to Jesus as the expected Messiah, the fulfillment of OT prophecy. He’s very cautious to conform to Jewish scruples of the day, even substituting “Heaven” for “God” with reference to the Kingdom. He repeatedly tells of something Jesus or someone connected with Him did and then adds the line “This was to fulfill the prophecy of …” or the equivalent. In extremely rough outline, he has (1) an Infancy narrative focusing on Joseph, (2) an account of Jesus’s ministry including five long topical sermons preached by Jesus, (3) a Passion story, and (4) accounts of Resurrection appearances. Supposedly he wrote first.
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Mark composes a gospel extremely similar to Matthew’s in many ways, using “Kingdom of God” and focusing on what Jesus did. Well over 90% of Mark is in very close parallel to part 2 of Matthew – but omits the lion’s share of the teachings, including the five long topical sermons. The two men even use identical language for about 30% of their text. Mark differs in not having an Infancy Narrative and in having a quite different Passion story and Resurrection appearances. (These may of course not be contradictions but the result of different choices in what to tell.) Mark emphasizes Jesus as the Son of God and the idea that He doesn’t want people to know that He’s the promised Messiah yet.
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Luke produces a gospel superficially similar to Matthew’s. But his Infancy Narrative focuses on Mary, he has a differerent Passion story and Resurrection appearances, and most importantly, while he follows the Matthew/Mark outline of Jesus’s ministry, he places the stories that he and Matthew share (but Mark omits) in quite different places for the most part, and sometimes with quite different meanings based on the context. (My standard example is to contrast Matthew’s Parable of the Talents with Luke’s Parable of the Pounds.) Luke’s portrait of Jesus is a man with compassionate concern for the poor and the outcast, and very much against legalism.
The problems, then: Why would Mark, supposedly writing based on Peter’s reminiscences, produce a Reader’s Digest Condensed Matthew that slavishly copies much of the narrative but omits most of the teachings, diverging from Matthew’s outline only at the climax of the story? Why would Luke take the same teachings as in Matthew but place them in very different locations, and sometimes with different points? What exactly are the relationships of these three stories that tell the same narrative but with significant differences in detail and extremely different emphases?
I do have an answer that does not involve presuming a “Q” never spoken of by early Christian writers. But before I present it, I’d like to see what you and your father have to say about those questions.