Several church fathers (i.e., Irenaeus, Origen, and Eusebius) stated what we might suppose from the distinctively Jewish emphases of this book, namely that Matthew wrote his Gospel primarily for his fellow Jews.21
He wrote, under the inspiration of the Holy Spirit, for a specific purpose or, more accurately, specific purposes. He did not state these purposes concisely as John did in his Gospel (John 20:30-31). Nevertheless they are clear from his content and his emphases.
"Matthew has a twofold purpose in writing his Gospel. Primarily he penned this Gospel to prove Jesus is the Messiah, but he also wrote it to explain God's kingdom program to his readers. One goal directly involves the other. Nevertheless, they are distinct."22
"Matthew's purpose obviously was to demonstrate that Jesus Christ was the promised Messiah of the Old Testament, that He fulfilled the requirements of being the promised King who would be a descendant of David, and that His life and ministry fully support the conclusion that He is the prophesied Messiah of Israel. . . .
"As a whole, the gospel is not properly designated as only an apologetic for the Christian faith. Rather, it was designed to explain to the Jews, who had expected the Messiah when He came to be a conquering king, why instead Christ suffered and died, and why there was the resulting postponement of His triumph to His second coming."23
Matthew presented three aspects to God's kingdom program. First, Jesus presented Himself to the Jews as the king that God had promised in the Old Testament. Second, Israel's leaders rejected Jesus as their king. This resulted in the postponement, not the cancellation, of the messianic kingdom that God had promised Israel. Third, because of Israel's rejection Jesus is now building His church in anticipation of His return to establish the promised messianic kingdom on the earth.
There are at least three wider purposes that Matthew undoubtedly hoped to fulfill with his Gospel. First, he wanted to instruct Christians and non-Christians concerning the person and work of Jesus.24Second, he wanted to provide an apologetic to aid his Jewish brethren in witnessing to other Jews about Christ. Third, he wanted to encourage all Christians to witness for Christ boldly and faithfully. It is interesting that Matthew is the only Gospel writer to use the Greek verb matheteuo, "to disciple"(13:52; 27:57; 28:19; cf. Acts 14:21 for its only other occurrence in the New Testament). This fact shows his concern for making disciples of Christ.25
Carson identified nine major themes in Matthew. They are Christology, prophecy and fulfillment, law, church, eschatology, Jewish leaders, mission, miracles, and the disciples' understanding and faith.26