Why certain people may have rejected term “Mother of God” hundreds of years ago is of no concern to me nor does it have any relevance to me. Jesus was the manifestation of God in the flesh, and that is who specifically the Bible calls Mary the mother of. The Bible does not refer to Mary as the Mother of God or the Queen of Heaven or any of the other Godlike titles Catholics like to give to Mary. God and the Son existed long before Mary, and to call Mary Mother of God needless confuses things.
Mary IS the mother of God. One cannot separate Christ’s humanity from his deity. This, in fact, is what raised the issue of Mary’s role at the Council of Chalcedon.
People came to the orthodox conclusions about Mary because of what was known by the orthodox to be true about Christ, but was denied by the Arians and others.
Marian doctrines always have Christological issues at their core; they’re not promulgated merely to magnify Mary further.