Mary was the mother of Christ in His humanity. She was not the "Mother of God". Christ is eternal. Mary is not. Christ existed long before Mary ever came on the scene.
This is elementary logic. Yet it seems to escape some.
Actually, you are operating with a false premise: “Christ is eternal.”
Jesus of Nazareth, or Jesus Christ (i.e., Jesus the Anointed), is NOT eternal. Jesus Christ was conceived in the womb of Mary, about 2000 years ago. Jesus of Nazareth, or Jesus Christ, BEGAN TO EXIST at that time.
Jesus of Nazareth is ONE PERSON. That Person is the eternal Word, or Son, of God the Father. He has existed from eternity in his divine nature. He began to exist in a human nature in the womb of Mary.
Is Mary the mother of one person, “the man,” and not the mother of some other person, “God”?
Jesus Christ is ONE PERSON. Thus, Mary cannot be mother of “the man Jesus” without being the mother of God.
Speaking of logic:
Mary is the mother of Jesus.
Jesus is God.
Thus:
Mary is the mother of God.
No one, ever, has propounded the idiotic notion that Mary is or was the mother of the eternal Triune Godhead. The title “Mother of God” has always meant only one thing: Mary is the mother of the Second Person of the Trinity by virtue of conceiving him in her womb so that he could begin to exist in a human nature.