People who refuse to acknowledge that Mary is the mother of God do so through asserting that Mary is mother only of the human flesh of Christ, thus they divide the person of Christ into two separate tings.
I disagree.
For me, and I think for most people, a mother is someone who gives birth to a baby and, for most of its life, is bigger than the child - has more authority, knowledge, is responsible for training the child etc.
Obviously Mary gave birth to Jesus. Jesus, as a human being, had a human mother.
But God needs no mother. Nobody made, or gave birth to, God - James says that God chose to give birth to US, James 1:18. God created and gave life to all things. Nobody brought God into being; no one nurtured him, taught him how to do things etc. So how can God have a mother? That implies there is someone greater than God. If he needed a mother, he is not all powerful.
Jesus was 100% man and 100% God.
Jesus, the human, had a mother who gave birth to him, brought him up, taught him to walk etc. Jesus' divine nature needed no mother - he always prayed, talked to and was guided by his Father. Both natures existed fully in Jesus.
How can that be? Who knows? But that's how it is.