What is St. Matthew's point with this important passage?
The first sentence of the Gospel according to St. Matthew is this: “The book of the generation of Jesus Christ, the son of David, the son of Abraham.” St. Matthew wants his readers to understand that Jesus is the Messiah, the Christ, and that in him are fulfilled all the promises made to Abraham (cf Genesis 22:15-18, “... and in thy seed shall all the nations of the earth be blessed”) and David (cf II Samuel 7, and the questioning of this promise in Psalm 89: “Lord, where are thy former lovingkindnesses, which thou swarest unto David in thy truth?" [v.49]).
It echoes also the similar “books of the generations” in the First Book of Moses: the “book of the generations of Adam” (5:1); the “generations of the sons of Noah” (10:1); “the generations of Shem” (11:10); “the generations of Isaac, Abraham's son” (25:19) and lastly “the generations of Jacob” (37:2). It places Jesus in the context of the Patriarchs; it further implies that he is not only the culmination of this long genealogy, but the beginning of something new, like unto Abraham, Isaac, and Jacob.
There would be many ways to trace the descent of a Jewish person from Abraham; all of them were his descendents, as were many others (e.g, the descendants of Ishmael). There would doubtless be many lines leading even from David to Jesus – St. Luke gives one which differs entirely from that of St. Matthew. But Matthew tracks the line through the kings of Judah. This is to show that Jesus is the legitimate Heir of David, “he that is born King of the Jews” (St. Matthew 2:2). But there is more: St. Matthew is reminding us of the Story. All of these people, from Abraham to Jechonias and his brethren at the time of the Exile, are known to us from the Old Testament. St. Matthew is making it crystal clear that Jesus is part of this Story and the culmination of it. In Jesus, the “author and finisher of our faith” (Hebrews 12:2) has himself entered the Story. Nothing can ever again be the same.
Now all this was done, that it might be fulfilled which was spoken of the Lord by the prophet, saying, Behold, a virgin shall be with child, and shall bring forth a son, and they shall call his name Emmanuel, which being interpreted is, God with us. (1:22-23)One final thought: This passage is one of the few glimpses we get of St. Joseph, “a just man” (v. 19). The Church begins with Our Lady St. Mary, who believed the words that had been spoken to her (St. Luke 1:45) and was the God-bearer, the Theotokos. But she was not alone: there were Elisabeth and Zecharias – and there was, after his vision in a dream, Joseph. He was at her side on that holy Night in Bethlehem; Joseph was with her, and with Him, as long as he lived; their shared belief in what had been shown them, and what was before their eyes every day, strengthened them through what was often a difficult and uncertain path. So it is today: we believe, and in our shared belief we strengthen one another.
What shall we do, that we might work the work of God? Jesus answered and said unto them, This is the work of God, that ye believe on him whom he hath sent. (St. John 6:28-29)