Matthew has long held this first position in the order of the four Gospels. This is because until very modern times, it was universally believed to be the first Gospel written and it was the one with the most developed connection to the Old Testament.
Though the precise occasion for the writing of this account is not known, it appears Matthew had at least two reasons for writing. First, he wanted to show unbelieving Jews that Jesus is the Messiah. Matthew had found the Messiah, and he wanted others to come into that same relationship. Second, Matthew wrote to encourage Jewish believers. If indeed Jesus is the Messiah, a horrible thing had occurred. The Jews had crucified their Messiah and King. What would now become of them? Was God through with them?
The Gospel of Matthew is filled with Old Testament quotations. This is undoubtedly because of the audience for whom the book was intended. Matthew primarily had Jews in mind as he wrote, and they would have been impressed by the many references to Old Testament facts and events. Quoting the Old Testament gave Matthew instant credibility with his Jewish audience.
Matthew began his Gospel with a record of Jesus’ genealogy because the Christians claimed that Jesus was the Messiah promised in the Old Testament. To qualify as such He had to be a Jew from the royal line of David (Isaiah 9:6-7). Matthew’s genealogy proves that Jesus descended not only from Abraham, the father of the Israelite nation, but also from David, the founder of Israel’s royal dynasty.
In his Gospel, Matthew sets out to show that Jesus is the long-expected Messiah of Israel, the only lawful Claimant to the throne of David.