According to Jewish tradition, there are two ways to determine the legitimacy of a King. One is Divine appointment, or prophetic secessionism, and the other is that the King-to-be must have a direct line of relation to King David. As a result, King David's genealogy is the only genealogy in the Bible that is tracked so thoroughly. His family tree is known as the Messianic Line.*

Since direct lineage to King David is required to be King, one can understand why Matthew went through the trouble of sharing Jesus' genealogy at the beginning of his Gospel. The genealogy listed in the Gospel of Matthew seeks to honor the Messianic Line tradition of appraising a King's legitimacy.

However, Matthew's genealogy more specifically traces the lineage of Joseph, not Jesus. And, while Joseph does share a direct relation with King David, through Solomon, Joseph is not Jesus' biological father; he is his adopted father. Thus, Joseph's genealogy is just narrowly irrelevant to the kingship of Jesus Christ.

What Matthew's genealogy does offer to Jesus' legitimacy as Messiah, however, is its unique inclusion of women. It breaks from Jewish tradition to include women in a genealogy, but Matthew seems to have been very intentional about the particular women with whom he decided to break this tradition. Matthew includes Ruth, Rahab and Tamar, as well as Bathsheba in the genealogy for Jesus Christ. Each of these women were Gentiles, and very much not of a royal Jewish line.

Ruth, Rahab, Tamar and Bathsheba are not only lifted up as vital contributors to the Messianic narrative by being named in Luke's genealogy of Jesus, but they solidify Jesus' status as a King for the people. These women make Jesus who He is.

*https://jewsforjesus.org/publications/issues/issues-v05-n06/the-genealogy-of-the-messiah

As mentioned above, according to Jewish tradition, there are two traditions which determine the legitimacy of a King. One is a direct relation to the Messianic Line of King David. The Gospel of Matthew addresses this requirement by providing Joseph's lineage, which traces all the way back to King David, but stops short at Jesus' birth because Jesus was not born of Joseph. This is where Mary saves the day (and humanity).

The other tradition which deems a King legitimate is Divine appointment, and that is precisely what Mary experienced when the angel Gabriel announced God's plans for her and her child. Jesus is a King two-fold because He meets the traditional requirements on both sides of His family: He is related to the Messianic Line through Joseph, His adoptive father, and He was Divinely Appointed through Mary.

Additionally, the family tree that is described in the Gospel Luke describes Mary's lineage - not Joseph's, like in Matthew. This is a counter-cultural move which gives Mary the seat of honor she deserves, as the mother of the Messiah. Jewish tradition only recognizes men in genealogies, and oddly enough, Luke's genealogy still gets away without mentioning any women, including Mary. However, through a careful study of the grammar and the names mentioned, it is clear that it is Mary's family tree that is traced, and not Joseph's.

Because Joseph's Messianic Line stops short at passing on to Jesus by virtue of not being his biological Son, Mary is the reason Jesus' Kingship was legitimate, according to tradition. She bridged the gap between millennia of tradition behind her, and millennia of salvation in front of her. Mary is the reason Jesus was King.