[Petrosius]

He is God but Mary is not the mother of the Father or the Holy Spirit. Hence the reason she’s not accorded mother of God.

The title "Mother of God" does not mean that she is the mother of the Trinity nor or the divinity of Jesus. Actually, this title is more about the person of Jesus than it is about Mary. There was an early heresy that Jesus was two persons, one divine and one human. The title "Mother of God" or Theotokos is used to show that Jesus has two natures, one divine and one human, but is one divine person. Since Mary is the mother of the one person who is Jesus, who is God, then she is the Mother of God.

[ealgeone]

The major problem with this logic is that the term “God” implies the totality of Yahweh, and we know that Yahweh has no beginning and no end (Psalm 90:2). First Timothy 6:15-16 says that God is immortal. Being immortal, God never was “born” and never had a “mother.” The second Person of the Trinity, Jesus, did have a beginning to His earthly ministry when he was conceived in Mary’s womb and was born, but from eternity past He had always been the Son of God.

A mother by definition precedes her child and at some point is more powerful than her child. So to call Mary the “mother of God” gives the misleading implication that Mary preceded and at one time was more powerful than the Lord God Almighty. Although Catholic doctrine tries to deny this implication, it is inescapable.

https://gotquestions.org/Mary-mother-God-theotokos.html