Why does Matthew's genealogy go back to Abraham instead of Adam?
Matthew traces Christ’s genealogy only to Abraham because Matthew presents Christ as the King. The promise of a coming King arises from the Abrahamic Covenant, not from anything promised to Adam. That King will rule and reign not only Israel but the whole world.
Les explains that Matthew’s Gospel opens by throwing the genealogy only back to Abraham, not to Adam. Matthew is one of the Gospels that presents Christ as the King. The whole concept of a coming King comes out of the Abrahamic Covenant, not from something God promised to Adam, but what He promised to Abraham. Therefore the genealogy in Matthew goes back to Abraham because he is presenting the King, the One who will rule and reign not only the nation of Israel but the whole world. By contrast, Luke’s Gospel chapter 3 genealogy goes all the way back to Adam, because Luke presents Christ not as the King but as the Son of Man, tying Him to Adam, the first man. Paul then refers to Christ as the second Adam.