Why would God bring the Savior into the world through a female virgin? Anselm offers some answers (Cur Deus Homo, 323-4):
“is extremely appropriate that, just as the sin of mankind and the cause of our damnation originated from a woman, correspondingly the medicine of sin and the cause of salvation should be born of a woman. Moreover, women might lose hope that they have a part in the destiny of the blessed ones, in view of the fact that such great evil proceeded from a woman: in order to prevent this, it is right that an equivalent great good should proceed from a woman, so as to rebuild their hope. Include this, too, in your picture: on the supposition that it was a virgin woman who has been the cause of all the evil besetting the human race, it is all the more appropriate that the woman who is to be the cause of all good should be a virgin. Another thing to include in your picture is this. One may presume that the woman whom God created from a man without a woman was created from someone who was a virgin: on this supposition, it is extremely fitting that the man who is to be created from a woman without a man, should be brought forth by a virgin. For the moment, however, let these considerations suffice with regard to the pictures which may be painted on the subject of how the God-Man ought to be born of a virgin woman.”
One guiding theological principle here is aesthetic: Salvation should stand in symmetrical relation with creation, redemption an fitting inversion of the fall. Another is pastoral: God has so arranged redemptive history as to give assurance to women that Eve’s sin has not left them hopeless.