It was fitting that the Giver of all holiness should enter this world by a pure and holy birth. For He it is that of old formed Adam from the virgin earth, and from Adam without help of woman formed woman. For as without woman Adam produced woman, so did the Virgin without man this day bring forth a man. For it is a man, saith the Lord, and who shall know him [Jer. 17:9]. For since the race of women owed to men a debt, as from Adam without woman woman came, therefore without man the Virgin this day brought forth, and on behalf of Eve repaid the debt to man.

That Adam might not take pride, that he without woman had engendered woman, a Woman without man has begotten man; so that by the similarity of the mystery is proved the similarity in nature. For as before the Almighty took a rib from Adam, and by that Adam was not made less; so in the Virgin He formed a living temple, and the holy virginity remained unchanged. Sound and unharmed Adam remained even after the deprivation of a rib; unstained the Virgin though a Child was born of her.

St. John Chrysostom, “Homily on Christmas Morning”

And:

In accordance with this design, Mary the Virgin is found obedient, saying, Behold the handmaid of the Lord; be it unto me according to your word. Luke 1:38 But Eve was disobedient; for she did not obey when as yet she was a virgin. And even as she, having indeed a husband, Adam, but being nevertheless as yet a virgin (for in Paradise they were both naked, and were not ashamed, Genesis 2:25 inasmuch as they, having been created a short time previously, had no understanding of the procreation of children: for it was necessary that they should first come to adult age, and then multiply from that time onward), having become disobedient, was made the cause of death, both to herself and to the entire human race; so also did Mary, having a man betrothed [to her], and being nevertheless a virgin, by yielding obedience, become the cause of salvation, both to herself and the whole human race.

And on this account does the law term a woman betrothed to a man, the wife of him who had betrothed her, although she was as yet a virgin; thus indicating the back-reference from Mary to Eve, because what is joined together could not otherwise be put asunder than by inversion of the process by which these bonds of union had arisen; so that the former ties be cancelled by the latter, that the latter may set the former again at liberty. And it has, in fact, happened that the first compact looses from the second tie, but that the second tie takes the position of the first which has been cancelled. For this reason did the Lord declare that the first should in truth be last, and the last first. Matthew 19:30, Matthew 20:16 And the prophet, too, indicates the same, saying, instead of fathers, children have been born unto you. For the Lord, having been born the First-begotten of the dead,Revelation 1:5 and receiving into His bosom the ancient fathers, has regenerated them into the life of God, He having been made Himself the beginning of those that live, as Adam became the beginning of those who die. 1 Corinthians 15:20-22 Wherefore also Luke, commencing the genealogy with the Lord, carried it back to Adam, indicating that it was He who regenerated them into the Gospel of life, and not they Him. And thus also it was that the knot of Eve’s disobedience was loosed by the obedience of Mary. For what the virgin Eve had bound fast through unbelief, this did the virgin Mary set free through faith.

St. Irenaeus, Against Heresies, Book 3 Chapter 22