Matthew used scripture to show Jesus was the promised Messiah. He used the scripture which, the people written to, should have easily pointed them to Jesus as the Christ. He wanted them to know so they would have every opportunity to turn and repent and be saved.
In the book of Matthew, Jesus is tied to the bloodline expected by the Jews who are the intended audience for this gospel. In light of this Jewish audience, Jesus’s identity as the fulfillment of the prophecies of the old testament (the long-awaited messiah) is important for Matthew to communicate clearly. For the Jewish community, establishing that Jesus’s story is the continuation of the Old Testament narrative is equivalent to proving that he is the foretold Messiah.
Right away, Matthew begins with the genealogy of Christ by focusing on connecting it to the old testament; specifically, he expresses the connection he has to Abraham and David and then goes on to describe him in chapter 1 of his book as Immanuel, “God with us.” This is so vital in demonstrating the fulfillment of Isaiah’s prophecy. I believe Matthew goes about it this way because of the fact that he wants to appeal to a Jewish mind set by demonstrating how the prophecy is fulfilled. If the Jewish people can’t see the evidence of the fulfilled prophecy, they can not see Christ as the true Messiah.
Matthew and Luke both introduce their gospels with the genealogy of Christ, but for different purposes. Matthew is concerned with Jesus’ earthly father, Joseph and his lineage, in an effort to link Jesus with the Old Testament prophecies and prove the fulfillment of the Old Testament prophecies as the Messiah. He refers to Hosea’s prophecy “ Out of Egypt I called my son.” (Hos.11:1), Isaiah’s prophecy of a prophet to lead the way of the Messiah (Is. 40:Matt. 3:3). This is important because Matthew attempts to prove that Jesus was exactly who he proclaimed to be, the Christ.