The Title, Mother of God, makes many non-Catholic Christians cringe. It is through their misunderstanding of the title and the Virgin Mary's role in the Catholic Church that the Catholic Church is implying that the Virgin Mary is part of the Godhead and older than Divinity. This misunderstanding and incorrect belief is not Catholic Church teaching. The correct Catholic Church teaching is this: Jesus, who is God the Son, was brought forth (not created) from God the Father, and who received His human nature by His human mother, Mary.
Jesus is God, made flesh. (John 1:1) Jesus who was in the form of God emptied Himself, taking the form of a servant, was born in the likeness of men. (Philippians 2:5-8)
The Virgin Mary deserves the title, Mother of God, because she carried Jesus, Who is God, in her womb. Her title does not imply she is part of the Godhead, nor imply that she is older than Divinity. The first person in Scripture to announce the Virgin Mary carrying God was St. Elizabeth. "And why is this granted me, that the MOTHER OF MY LORD should come to me?" (Luke 1:43)
We also see the familiar Nativity scene in Scripture of Baby Jesus who was just born and being visited by wise men. "...and going into the house they saw the child with Mary his mother, and they fell down and WORSHIPPED him...." (Matthew 2:11) Non-Catholic Christians would agree that "worship" belongs to God alone. And in this Scripture we see baby Jesus being worshipped because He is God. Therefore, the Virgin Mary who had just given birth to baby Jesus would be "Mother of God." There is no way of denying this title given to Mary of Christological truth, unless we deny the Virgin Mary gave birth to Jesus, or deny Jesus is God.