Why does Matthew's genealogy start at Abraham instead of Adam?
Matthew traces Christ's lineage from Abraham because that Gospel presents Christ as the King. The promise of a coming King who will rule Israel and the whole world flows from the Abrahamic Covenant, not from anything God promised Adam. So the genealogy begins with Abraham to emphasize Christ's royal, covenantal right to reign.
Les explains that Matthew is one of the Gospels that presents Christ as the King. In Matthew's very first verse, the genealogy goes only back to Abraham, not to Adam, because the whole concept of a coming King comes out of the Abrahamic Covenant. It does not come out of something God promised to Adam, but out of what He promised to Abraham. Matthew is therefore presenting the King, the One who will rule and reign not only the nation of Israel but the whole world. This fits the broader context of Isaiah's prophecy of the Prince of Peace, whose government rests on His shoulder and whose peace has no end upon the throne of David.