You say: A mother, by definition, PRECEDES her child...
FALSE: A mother, by definition, provides the ovum, gestates, and gives birth to her child.
Mary provided the ovum, gestated, and gave birth to Jesus Christ, so that hem the Second Person of the Trinity, could live in the world as man.
Because Jesus Christ is God, the Second Person of the Trinity, Mary is called “the Mother of God,” precisely as Mary is the mother of a carpenter, the mother of a Jew, the mother of a preacher, etc.
Because Jesus Christ is not God the Father, Mary is not the Mother of God the Father. Because Jesus Christ is not the Holy Spirit, Mary is not the Mother of the Holy Spirit. Because Jesus Christ is not the Trinity, Mary is not the Mother of the Trinity.
Because Jesus Christ is God, Mary is the Mother of God. She became the Mother of God IN TIME, at the moment when the eternal Word became flesh in her womb.
More Catholic logic?? I’ve seen you’re arguments before and they aren’t grounded in solid Scripture.