Because "God" and "Father" are not identical.
Isn't it more correct to just call Mary what the Bible calls her - The Mother of Jesus. She is never given such an exalted title in Scripture or any of her other exalted titles other than blessed. She is called the Mother of Jesus.
That's exactly what Nestorius wanted to call her. That title, however, denies Christ's divinity. As I explained above (#1656), denying that Mary is the mother of God logically entails one of three heresies.
-A8
It doesn't deny Christ's divinity. It denies Mary's motherhood of God. Jesus was divine because He was God. He would have been God without Mary's ever having existed. He would have been God if he were never incarnated.
As to God and Father not being identical - are you now separating the Father from the Godhead??? Or are you backtracking and saying the Father is only a part of the Godhead and can be separated from the Son? (i.e., component parts of the one unit)