Just to clarify...this syllogism you are using falls apart simply because Jesus is not ALL OF GOD (meaning that he is the second person of the triune Godhead). Using your logic it would be like saying:
Mary is the mother of Sam. Sam is a fireman. Therefore, Mary is the mother of firemen. Get it?
Mary is the mother of Sam. Sam is a fireman. Therefore, Mary is the mother of firemen. Get it?
The title "mother of God" means that Mary is the mother of God the Son, the Word, the Second Person of the Trinity, because she conceived him in her womb and bore him. It has NEVER meant that Mary is the mother of God the Father and/or God the Holy Spirit.
In other words, you are arguing against an assertion that NO ONE HAS EVER MADE--namely, that Mary is the mother of the Trinity or the mother of one or both of the other Persons of the Trinity.