The hypostatic union of Christ’s two natures is the issue here. No one can explain and it and no one expects you to. However, Mary is still the mother of God since Jesus isn’t split into two parts. Mary gave Jesus his human nature and the Holy Spirit gave Jesus His divine nature. Since Jesus is truly man and truly God, and Mary is his mother, Mary is also the mother of God. This does not make her a God herself, and the concept is perfectly benign and not should not cause issues.
Jesus is one person with two natures. Mary is the mother of Jesus, who was both true man and true God. Mary did not give birth to a nature, but to a person. Mary is the mother of Jesus. Rather than mother of God, you might as well say she's the mother of man. It makes as much sense.
Since God is triune, He exists in 3 persons. To call Mary the mother of God seems wrong. She is the mother of the son of God. She did not birth the father. She did not birth the holy spirit. I realize this term was from the early 200's, but it still sits wrong.
So Mary is the mother of God, as in the son of God. Mary is not the mother of God, as in the triune God.
The thing is, this does not affect our salvation. There isn't anything more interesting than discussing religion, but at the end it is Jesus and His death on the cross that atoned for our sins. So I try to steer away from discussions like the one in this thread, but sometimes I am too weak and feel like I have to make my voice heard.
I think I am going to put a sign over my monitor saying looking unto Jesus, the author and finisher of our faith (Heb. 12:2) That's all that really matters.