Mary is not the origin of the eternal Word, the Second Person of the Trinity. No one ever believed or said that she was.
Mary IS the mother of Jesus Christ. Jesus Christ is the incarnate Word, the Second Person of the Trinity.
Because Jesus Christ is the Second Person of the Trinity, who is God, Mary is called the “Mother of God.”
Which, by Catholic admission, is the only nature of Jesus that is divine. Mary is not the origin (aka mother) of the divine God.
Mary is the mother of the Incarnate word, not the second person of the trinity.
Therefore she is the mother of Jesus, not the mother of God.