Good thread, aspen. I agree.
Look at it this way.
1. Jesus is God.
2. Mary is the Mother of Jesus.
If we accept these two things as truth, and any Christian worth his salt does, one of two things must be true.
Either
A) Mary is the Mother of God. If you really prefer saying "Mother of the Second Person of the Trinity, which is God" then that is fine.
or
B) Jesus is not God.
So which one? The Jehovah's Witnesses and the Mormons, in their disdain for Mary, have resorted to choosing B).
If all your premises are completely true, then yes, the conclusion must also be true. Your first premise is only half-true, though.
Jesus, while on earth, was a man. Humans are made up of three things: spirit, soul, and flesh. Everything is created by God, of course, but the flesh is something created here on earth. My flesh(physical body) is made up by a combination of my mom's and dad's flesh. Their DNA created my DNA. My physical body is permanently marked by the "fingerprint" of my paternal/maternal parents.
My mind(soul) is my own. Certain science says certain personality traits and such are inherited, while other science says my personality, intelligence, etc are a product of my environment (nature vs nurture). Either way, this is mostly something that society helps to mold me into. It is something not inherited, then, but learned. One could say, then, that part of my soul is the product of my parents, and so they could partially be the parents of my soul.
My spirit is not my own and it is not inherited from my parents. Only God can create a spirit. Satan can be the spiritual father until we turn our lives over to God, but only God can create it. So, God is the paternal father of our spirits, while Satan is the adopted father of certain spirits. When we are reborn in Christ, God becomes the Father of our spirits once more. Notice, God is the Father of the spiritual.
Mary gave birth to Jesus(physical and arguably mental). God, however, created the spirit. No amount of DNA combinations given by Mary can ever create a spirit. All Mary's DNA can give us is Jesus' physical body and arguably part of his soul. The spiritual part of Jesus (the part that contains His "God") came directly from God.
So, no Mary is not the mother of God. She is simply the mother of the fleshly shell of Jesus that contained his spirit.
The argument would then be:
Jesus was man and spirit on earth
Mary gave birth to Jesus' physical being
Mary is the mother of Jesus-in-the-flesh