But when the time had fully come, God sent forth his Son, born of woman, born under the law, to redeem those who were under the law, so that we might receive adoption as sons. And because you are sons, God has sent the Spirit of his Son into our hearts, crying, "Abba! Father!" So through God you are no longer a slave but a son, and if a son then an heir. - Galatians 4:4-7

A God who was not only God, and a man who was not simply man, was born of woman. 

By being born he formed the gate of salvation from what had at one time been the way in for sin. Where in fact the serpent by exploiting human disobedience had infused his poison, there the Word entered through obedience and built a living temple. From the womb of a woman had come forth the original son of sin, Cain; and from the womb of a woman, without seed, there came into the light the Christ, the redeemer of the human race. 

Let us not be ashamed that he was born of a woman. That birth was for us the beginning of salvation. 

If Christ had not been born of woman, he would not have died either, and would not 'by death have destroyed him who had the power of death, that is, the devil.' [Heb. 2:14] 

[from Homily on the Mother of God (PG6S, 679ff.)]
 
 

Quotes from early church fathers on the Incarnation » If Christ had not been born of woman, by Proclus of Constantinople  » When Christ comes, God will be seen by men, by Irenaeus » The Word made flesh deifies us, by Hippolytus » Life itself appeared in human form, by Augustine of Hippo