Did the Virgin give birth to Man or God by St. Cyril of Alexandria.

” Christ was born God and man and this the Virgin is both Christotokos and Theotokos. But, in case they say that the indwelling is a union not in the Virgin, but after the birth from her had taken place, bring and let us examine this saying as well. Is it because of this sort of indwelling that the anointing is applied to the person of the Logos? They will say that because the man existed together with and is united (understood in their sense) to the Logos, it is necessary to say that He was anointed with the union. For the prophet and also the Apostle spoke of God the Logos as God and openly attributed to him the anointing. If, then, because of the union and the coexistence with the man, the saints attach to the Logos what is proper to man, they should in any case confess that this anointing took place after the union. Now, if he were anointed after the union and they do not want to speak of the union before the Virgin delivered, they should no longer call the Virgin Christotokos (Christ-bearer). For if she is Christotokos, she must also be Theotokos (God-bearer), and if she is not Theotokos, neither is she Christotokos.

But if the anointing is after the union, and it is for this reason that it is mentioned in reference to the person of the Logos, and if they say that the union took place after the birth from the Virgin, then she shall no longer be found to be Christotokos. On the other hand, if she is Christotokos, then she is also Theotokos. For, since the anointing cannot be conceived before the union, if the Virgin is Christotokos, because the union took place in her, she no longer gave birth to a man, as they say, but to one united with the Logos, and she would justly be called Theotokos.”

Cyril of Alexandria,
Against those who are unwilling to confess that the Holy Virgin is Theotokos 9.