Why does Matthew’s genealogy go back to Abraham, while Luke’s goes back to Adam? Matthew is very concerned with showing that Jesus is the fulfillment of the promises that God made to the Jewish people through both Abraham and David. However those promises don’t just show that Jesus is the coming King of the Jews (2 Samuel 7:12), He is also the Savior of the world. As God said to Abraham: “I will bless those who bless you, but the one who treats you lightly I must curse, so that all the families of the earth may receive blessing through you” (Genesis 12:3). Which is one of the reasons we see Gentiles like Tamar, Rahab, and Ruth mentioned in the genealogy: Jesus is the Savior for all!
For worship: https://www.youtube.com/watch?v=tdxSC1tHJn0