Genealogies may be sport-like hobby for us, but for them it was the structure of their society. In a culture organized around family relationships, a careful list kept in the house, and passed from generation to generation, determined a person’s social relationships. Rulers in particular used genealogies to justify their power, rank, and status.
But we also have to understand this about their culture and family lists: it wasn’t as important to be complete as it was to accomplish the purpose in keeping all the statistics. Matthew records a genealogy also, and his resembles the kind kings kept to show they were the rightful kings. Matthew arranges his list into 3 groups of 14 names each, because he’s trying to prove a point more than he’s trying to be thorough and all-inclusive. Luke has an agenda also. Notice his list concludes with, “…the son of God.” Hmm. Matthew excludes certain names to fit his purposes of showing Jesus’ royalty, and he makes a point even in the numbers in each group. Luke is more inclusive, posting many more common names, probably trying to show us that Jesus is just like us, and that he came for all humankind. Luke ends with Adam, “the son of God,” and then takes us immediately to the temptation scene to show us that Jesus is different from Adam, and that he is “the Son of God” in a different way: like us, and yet without sin.