Matthew’s gospel opens with a list of “begats” tracing Joseph’s lineage back through David to Abraham. How is this relevant, considering that the Holy Ghost is the father of Jesus? Why do they not give us Mary’s lineage?
The genealogy in Matthew 1 is a royal genealogy, and as such it has several features of such ancient genealogies. For one thing, it is schematized and does not include all the generations. For another, it reflects the Jewish practice that if a man adopted a son, then he was entitled to his stepfather’s genealogy, even though he wasn’t physically his offspring. In the case of Jesus, this meant when Joseph accept him as his son he was entitled to Joseph’s genealogy. The author does not give us Mary’s genealogy because we are dealing with a patriarchal Jewish culture, where the father’s genealogy is all-important.
—Ben Witherington III