Mary’s title “Mother of God”
This one is ancient, dated back to the early Church. It is called the “Nestorian heresy”. Nestorius claimed that “Mother of God” or “Theotokos” in Greek, bestows divinity on Mary and so cannot be accepted. He proposed “Mother of Jesus”. This was definitively defeated at the Council of Chalcedon.
Jesus is both God and man, completely man and yet completely God; the two cannot be divided. Mary is mother of Jesus, who is God. “Son of God” and God the Father and the Holy Spirit are three Persons but is only one God, inseparably one. To call Mary “Mother of Jesus”, or even “Mother of God’s Son” and not “Mother of God” would be artificially trying to separate the divinity of Jesus from the humanity of Jesus, a heresy in itself.
If God who is purely divine can become completely human without losing his divinity, then Mary a mere human, can certainly become the Mother of pure divinity.