Matthew’s main purpose in writing his Gospel (the “good news”) is to prove to his Jewish readers that Jesus is their Messiah. He does this primarily by showing how Jesus in his life and ministry fulfilled the Old Testament Scriptures.
Matthew, surnamed Levi, before his conversion was a publican, or tax-gatherer under the Romans at Capernaum. He is generally allowed to have written his Gospel before any other of the evangelists. The contents of this Gospel, and the evidence of ancient writers, show that it was written primarily for the use of the Jewish nation. The fulfilment of prophecy was regarded by the Jews as strong evidence, therefore this is especially dwelt upon by St. Matthew. Here are particularly selected such parts of our Savours history and discourses as were best suited to awaken the Jewish nation to a sense of their sins; to remove their erroneous expectations of an earthly kingdom; to abate their pride and self-conceit; to teach them the spiritual nature and extent of the gospel; and to prepare them for the admission of the Gentiles into the church. Matthew Henry