Augustine of Hippo — as excerpted in the Catena Aurea on Matthew 1:2

“(De Cons. Evan. ii. 1.) Matthew, by beginning with Christ’s genealogy, shews that he has undertaken to relate Christ’s birth according to the flesh. But Luke, as rather describing Him as a Priest for the atonement of sin, gives Christ’s genealogy not in the beginning of his Gospel, but at His baptism, when John bare that testimony, Lo, He that taketh away the sins of the world. (John 1:29.) In the genealogy of Matthew is figured to us the taking on Him of our sins by the Lord Christ; in the genealogy of Luke, the taking away of our sins by the same; hence Matthew gives them in a descending, Luke in an ascending, series. But Matthew, describing Christ’s human generation in descending order, begins his enumeration with Abraham.”