1. God has always existed and created all things
2. God created Mary
3. Mary is a Jewish virgin
4. God took on human form through being born of a virgin, Mary
5. Mary is the mother of the incarnated God - TRUE
6. Mary is the mother of God - FALSE
Yep, that's what the Church teaches. We call the incarnated God "God".
Well, okay, as long as we clarify that the Incarnate God is indeed God and then delineate the distinctions between "the Incarnate God" and "God." Because, formally, 5 and 6 necessarily imply that the Incarnate God is not God.
If that is satisfactorily done, then Prop 6 is okay except that for umpty-ump years the distinction HAS been drawn and of the two optional articulations "mother of God" won.
A common formulation of the Trinity:
The Father is NOT the Son and NOT the Spirit.
The Father is God.
The Son is NOT the Father and NOT the Spirit.
The Son is God.
The Spirit is NOT the Father and NOT the Son.
The Spirit is God.
There are not three Gods, but
There is one God.
Jesus is the Incarnate Son of God. He is "Dominus meus et Deus meus," as Thomas says without rebuke.
To the extent that Thomas is right to say,"... ο θεος μου." [ho theOS-moo, (the 'the' has an unvoiced th, as in "thing", and the 'e' is like 'eh'-- so I was taught FWIW.)] to that extent Mary is the Mother of God.
Had Thomas said "Trinity" or "Father" or "Spirit", he would have been wrong, and to that extent Mary is NOT the mother of God.
I don't see what's wrong with that.
But, as I may have said one or two times already, if it's good enough for the Church at Ephesus and Chalcedon it's good enough for this dawg.