I have come across protestants who take issue with calling Mary the mother of God in reference to being the mother of Jesus. They deem it too “catholic” sounding, or something. But to deny this proper title to Mary is to deny the divinity of Jesus Christ and to resurrect old heresies. Mary is clearly referred to as the Mother of Jesus, the Mother of the Lord, the mother of God. Jesus Christ clearly claimed to be God in the Flesh, the Son of God, the second of the Triune God, the Father, the Son, and the Holy Spirit.
When Elisabeth greeted Mary in Luke 1:43 she exclaimed, “And whence is this to me, that the mother of my Lord should come to me?” The Greek word for Lord is “kurios,” (koo-ree-os). It means Supreme in authority. The word “God” would be interchangeable.
There are also many other scripture references that refer to Mary as the mother of Jesus, who I would remind you is God in the flesh.
Matthew 1:18, Luke 2:43, John 2:1, John 2:3, John 19:25, Acts 1:14, Matthew 2:13, Luke 1:15.
Yes, the Word of God existed from all eternity. He did not find His beginning in the womb of the Virgin. However, He took the form of man, was conceived, and took on fully our nature. In His flesh He is fully God and fully Man without division. Mary bore the Son of God. She was His mother. He was flesh of her flesh. In this sense she was very much the Mother of God, the Son of God, the Word who became one of us.
The Athanasian Creed makes this statement,
"He is God from the essence of the Father, begotten before time; and he is human from the essence of his mother, born in time; completely God, completely human, with a rational soul and human flesh; equal to the Father as regards divinity, less than the Father as regards humanity. Although he is God and human, yet Christ is not two, but one. He is one, however, not by his divinity being turned into flesh, but by God's taking humanity to himself. He is one, certainly not by the blending of his essence, but by the unity of his person. For just as one human is both rational soul and flesh, so too the one Christ is both God and human."
Because the second Person of the Triune God, the Word, took on flesh and was truly born fully human as much as He is fully God by the Virgin Mary, she is truly the Mother of God. To deny this is to deny one of the primary and most important doctrines of the Christian faith. To deny it is to deny the faith.