You will note that I said “denied.” That is not at all the same as never having used the title.
This is exactly what you said:
"Anyone who says that Mary is not the mother of God has to deny that Jesus is God.
I wonder if you can comprehend that someone can believe that Jesus IS God in the flesh, that He IS the Son of God who existed for all eternity yet refuse to refer to Mary as the "Mother of God"? If you are going to make acceptance of that title a matter of salvific doctrine and call everyone who disagrees with you a heretic, then you really ought to show a solid Scriptural basis for it. And the teaching that Mary is the mother of Jesus Christ who is the Son of God in the flesh is NOT the same thing.