Well, yes! SHOCK!!! SHOCK!!!
Have you ever read the first chapter of the Gospel of John?
The Word, God the Son, the Second Person of the Trinity, BECAME FLESH and dwelt among us!
Since Jesus is God, and Mary is his mother, she is called the Mother of God. In order to deny that Mary is the mother of God, you have to be able to believe that a woman can have a son who is God without being the mother of God. Or, you have to simply deny that the son of Mary is God. Or, you have to deny that Mary ever had a son.
Can a woman have a son who is a fireman without being the mother of a fireman?
That is just about the worst attempt at apologetics I think I've seen from catholicism.