good points. Also, note that your mother didn’t create you, my mother didn’t create me and Jesus’ mother didn’t create him. These marvelous women bore their children — their children came from God and in Jesus’ case, WAS/IS God
Of course, our mothers and fathers pro-create our bodies and do not pro-create our souls. Mary’s body was involved in the pro-creation of the body of Jesus. His human soul was a special creation, just like ours, and his Divine Person existed eternally.
Mary was/is the mother of Jesus.
Jesus is God.
Thus, it makes perfect sense to call Mary “the mother of God.” She is the mother of a person who is God the Son. A person who is God the Son is her son. She is the mother of God the Son. She is the mother of God.
If Mary is the mother of Jesus, it is self-evident that Mary is the mother of God.
The only conceivable reason anyone would refuse to call Mary the mother of God is that that person is filled with hate for Mary. Where that hate came from I do not know, although propaganda seems a likely candidate.