Why don’t Jesus’ genealogies in Matthew 1 and Luke 3 match?
Matthew was writing to the Jews and Luke to the Gentiles. Matthew was concerned with the paternal line, as a good Jew would be. He tracks down the royal family tree to prove that Jesus is the King of the Jews. He starts with the first Jew, Abraham, and follows right along the line to David, the first king from Judah’s line, and tracks all the way to Joseph, the legal father of Jesus.
Luke, however, is a doctor writing to Gentiles. He’s out to prove that Jesus is the Son of Man. His genealogy runs backward and tracks Jesus’ lineage from Adam, the first man, through to Mary. The term “as was supposed” in verse 23 is the Greek word “numizo” which means “reckoned by law.” Joseph was Heli’s son-in-law, not his son.
There’s another interesting difference. Matthew gets to David and then takes the first surviving son of Bathsheba, Solomon, to get to Joseph. Luke takes the 2nd surviving son of Bathsheba, Nathan (no not the prophet Nathan, a different Nathan). This avoids a rather nasty mess mentioned in Jeremiah 22:30. More on that later.
Source: Missler, Chuck. Learn the Bible in 24 Hours. Koinonia House.