Matthew called Jesus the Son of Abraham and the Son of David (Matthew 1:1).
God promised Abraham that all of the world would be blessed through him and his descendants (Genesis 12:3). The promised Messiah would descend from him. God promised David that his throne would last forever (2 Samuel 7:16). The promised Messianic king would be his ultimate heir.
The genealogy in Matthew
The genealogy in Matthew, chapter one, includes the great patriarchs, Abraham, Isaac and Jacob. It includes members of the tribe of Judah, the tribe given leadership among the Jews (Genesis 49:10). It concludes with a list of the line of David, first the kings of Judah and then the line in seclusion after the Babylonian Captivity. The genealogy shows that through two thousand years of Jewish history God preserved the promised line from Abraham through David to Jesus. History is full of royal lines that ended. This one was preserved.
The list also includes the unexpected. It includes four women.
Tamar was a Canaanite who posed as a prostitute to get what Judah should have provided (Genesis 38).
Rahab was a Canaanite who was a prostitute but believed in the true God and was saved from the destruction of Jericho (Joshua 2; Hebrews 11:31; James 2:25).
Ruth was a Moabite who left her cursed nation and lived in humble faith in the God of her mother-in-law. (Ruth; Deuteronomy 23:3)
Bathsheba is not even called by name. She is named Uriah’s wife to remind the readers of her seduction by the great King David and the murder of her husband by the fabled leader (2 Samuel 11; 12).
Sarah and Rebecca would have been more likely inclusions but they are unmentioned.
Messiah came from a truly human line.
Foreigners, adultery, murder, cursed peoples and seduction are all part of His background.
Jesus came to save an imperfect humanity.
Matthew did not leave out embarrassing details when he began his case that Jesus was the Messiah, the only Savior of the world.