I have always been bothered by that phrase...God exhisted quite some time before Mary was born...Therefore,it's impossible that Mary is the mother of God...
Mary 'is' the mother of the human baby, Jesus...Mary was the mother of Jesus, the prophet...Jesus/God was not born of Mary...Jesus/God has always been...Jesus/man was born of mary...Jesus/King/God will show up soon and He will be in appearance as He really is...And I doubt he will have long blond hair and a trimmed beard...
Seems this Mother of God thing is too close to the old Isis, Osirus story where the mother (queen of heaven) married the king and later she married her own son (wasn't he the Sun God?)...And to this day, you see the Catholic representations of Mary with a glowing sun around her head...
If you deny that she is the Mother of God, then you deny Jesus' divinity. The "Mother of God" title (Theotokos), rather than a device to glorify Mary, was orginally really a way of defending against the Arian heresy.
Obviously, God has no beginning and no end, so He existed before He was born of woman. That does not take away from the very real fact that He chose to be born of Mary.
Mary is/was the mother of God. The fact that God existed before she was born is irrelevant.
The phrase "Mother of God" is even contained in the "Hail Mary." Strange that the phrase should bother you so.