St. Cyril of Alexandria: Theotokos - Mother of God

Let not any be troubled, hearing the holy Virgin called Mother of God, nor let them fill their souls with Jewish unbelief, yea rather with Gentile impiety. For the Jews attacked Christ saying, For a good work we stone Thee not but for blasphemy because Thou,being a Man, makest Thyself God: and the children of the Greeks, hearing the doctrines of the Church that God hath been born of a woman, laugh.

But they shall eat the fruit of their own impiety, and shall hear of us, The fool will utter folly and his heart imagine vain things. But the plan of our Mystery, albeit to the Jews it be an offence, to the Gentiles folly, yet to us who know it, verily admirable is it and saving and far removed from being to be disbelieved by any. 

For if there were any whatever who should dare to say that this flesh made of earth had become mother of the bare Godhead, and that she bare out of her own self the Nature which is over the whole creation, the thing would be madness and nothing else: for not of earth has the Divine Nature been made, nor will that which is subject to decay become the root of immortality nor that which is subject to death bear the Life of all things, nor yet the Unembodied be the fruit of the palpable body, that which is subject to birth [bear] that which is superior to birth, that which hath its beginning in time, that which is without beginning.

But since we affirm that the Word became as we and took a body like to our bodies and united this of a truth unto Himself, in a way namely beyond understanding and speech, and that He was thus too made Man and born after the flesh, what is there incredible therein or worthy of disbelief? albeit the human soul (as we have already full often said) being of other nature than the body, is yet born with it, just as we say that it too has been united therewith. Yet will no one (I deem) suppose that the soul has the nature of the body as the beginning of its own existence, but God inplaces it ineffably in the body and it is born along with it; yet do we define as one the animal that is made up out of both, i. e., man. 

Therefore the Word was God but was made Man too, and since He has been born after the flesh by reason of the human nature, she who bare Him is necessarily Mother of God. For if she have not borne God, let not Him Who is born of her be called God; but if the God-inspired Scriptures call Him God, as God Incarnate and made Flesh, and it be not possible in any other way to be Incarnate, save through birth of a woman, how is she not Mother of God, who bare Him?

 (Scholia on the Incarnation 28)