Why was it necessary for Jesus to have been born of a woman?
Vatican II responds:
The Father of mercies willed that the Incarnation should be preceded by assent on the part of the predestined Mother, so that just as a woman had a share in bringing about death, so also a woman should contribute to life. This is preeminently true of the Mother of Jesus, who gave to the world the Life that renews all things, and who was enriched by God with gifts appropriate to such a role. (Lumen Gentium 56)
She is the virgin woman whom the prophet Isaiah said would conceive and bear a son (cf. Is 7:14; Mt 1:23). And she is Mary, who, being immaculately conceived, remained sinless. It was through her consent—and her humility as handmaid of the Lord—that she gave Jesus his body, and his body is what saved us.
Pope John Paul II wrote in Mulieris Dignitatem:
"When the time had fully come, God sent forth his son, born of woman." With these words of his Letter to the Galatians (4:4), the apostle Paul links together the principal moments that essentially determine the fulfillment of the mystery "pre-determined in God" (cf. Eph 1:9). The Son, the Word, one in substance with the Father, becomes man, born of a woman, at "the fullness of time." This event leads to the turning point of man’s history on earth, understood as salvation history. It is significant that St. Paul does not call the Mother of Christ by her own name "Mary," but calls her "woman": This coincides with the words of the Protoevangelium in the book of Genesis (cf. 3:15). She is that "woman" who is present in the central salvific event, which marks the "fullness of time": this event is realized in her and through her. (MD 3)