Tract from Catholic Answers
A woman is a man’s mother either if she carried him in her womb or if she was the woman contributing half of his genetic matter or both. Mary was the mother of Jesus in both of these senses, because she not only carried Jesus in her womb but also supplied all of the genetic matter for his human body, since it was through her—not Joseph—that Jesus “was descended from David according to the flesh” (Rom. 1:3).
Since Mary is Jesus’ mother, it must be concluded that she is also the Mother of God: If Mary is the mother of Jesus, and if Jesus is God, then Mary is the Mother of God. There is no way out of this logical syllogism.
Although Mary is the Mother of God, she is not his mother in the sense that she is older than God or the source of her Son’s divinity, for she is neither. Rather, we say that she is the Mother of God in the sense that she carried in her womb a divine person—Jesus Christ, God “in the flesh” (2 John 7, cf. John 1:14)—and in the sense that she contributed the genetic matter to the human form God took in Jesus Christ.
“The Virgin Mary, being obedient to his word, received from an angel the glad tidings that she would bear God”
Irenaeus (Against Heresies, 5:19:1 [A.D. 189]).
“Being perfect at the side of the Father and incarnate among us, not in appearance but in truth, he [the Son] reshaped man to perfection in himself from Mary the Mother of God through the Holy Spirit”
Epiphanius of Salamis (The Man Well-Anchored 75 [A.D. 374]).
“When, therefore, they ask, ‘Is Mary mother of man or Mother of God?’ we answer, ‘Both!’ The one by the very nature of what was done and the other by relation”
Theodore of Mopsuestia (The Incarnation 15 [A.D. 405]).