I'd like to explore some neglected considerations regarding the compatibility of Matthew and Luke's genealogies:
1. Liberals take one of two positions:
i) Matthew and Luke are using independent, divergent traditions. There's no reason to believe either tradition is historically reliable.
ii) Matthew and Luke fabricated the genealogies.
Conservative attempts to harmonize the two genealogies are chalked up to special pleading.
2. Let's begin with a personal anecdote. I have a cousin who has three daughters. By definition, I'm a generation older than her daughters, yet her daughters are older than me! Sounds like a riddle. How is that possible?
My cousin and I share common ancestors in our maternal grandparents. They had 9 children, covering a 14 year spread. She and I are children of their children.
She's about 25 years older than me, and she married at 15. As a result, her daughters were born before I was born.
Even though I belong to the same generation as their mother, they are older than me. Seems contradictory that people who are a generation younger than me can be older than me, but that's one of those wrinkles you run across in real life.
And you can imagine this might be confusing to a reader who didn't have all the information. Indeed, it might seem like a discrepancy!
3. Suppose we compare two lists of people that both terminate with Queen Elizabeth II. They have a few names in common, especially towards the end. But most of the names don't match. On the face of it, these are discrepant, indeed, irreconcilable lists. Although they converge near the end, they are mostly divergent.
But in principle, both could be correct. You see, one could be her family tree while the other could be the royal succession. One list could be genealogical while the other list could be dynastic.
In one sense, the two lists cannot be harmonized. Most of the names don't match. Yet the two lists are indirectly interconnected because both lists are related to Queen Elizabeth. The names aren't related to each other, but to her. They both list predecessors, but two different kinds of predecessors. One list is based on biological descent while the other is based on dynastic descent. One is a list of rulers while the other is a list of ancestors. Both lists could be diagrammed as trees, but they operate on different principles.
They can't be combined because they employ different selection criteria. Yet the two lists are mutually compatible.
There are, of course, stretches during which biological lines and royal lines overlap. But although the royal lineage is continuous, the biological lineage is discontinuous inasmuch as dynasties may die out, or be abruptly supplanted by a rival house. Because the royal families of Europe and Great Britain intermarried from time to time, the two lists will intersect at random points.
Now, imagine if you had a copy of both lists, but they weren't labeled. One wasn't entitled the rulers of Great Britain and the other wasn't entitled the family tree of Elizabeth II. You just had a sequential list of names. It would be very puzzling to compare the two lists. Puzzling to discern a unifying principle. You have no overarching context. Just two bare lists.
Imagine if these lists were 2000 years old. Your knowledge of that period is full of gaps. Historical records that identify names on the list are quite fragmentary.
It would be easy to conclude that one or both lists are inaccurate, contradictory, legendary, or fabricated. Yet that would be an ignorant conclusion.
4. Apropos (3), does "beget" language (X begat Y) entail a genealogical relationship? Not necessarily. The same language can be figurative to denote a dynastic relationship, viz. 2 Sam 7:14, Ps 2:7. God was not David's literal progenitor.
So when we read the "genealogies" of Christ, are these consistently biological precursors, or might they sometimes be royal precursors? Keep in mind the Davidic emphasis, not only in the Matthean "genealogy," but Matthew's Gospel generally.
5. And here's a final wrinkle. Biblical lists of people aren't necessarily arranged according to a single structuring principle or selection criterion. Take the Table of Nations (Gen 10). Is the linkage genealogical, geographical, or socioeconomic? Seems to be some of each.
That should perhaps forewarn us not to presume that the "genealogies" of Christ in Matthew and Luke are reducible to a single type of affinity.