Dear xzins,
One may certainly say that Mary is the Mother of Jesus. One may also certainly say that Mary is the Mother of the Christ.
However, if one says that Mary is the Mother of Jesus, the Mother of the Christ, but then specifically says she is NOT the Mother of God, then one is denying His Divinity.
If Jesus is God and Mary is His Mother, then she is the Mother of God. Jesus is a single individual, not two. He HAS two natures, but IS one person. Mary is mother of a person, not a nature. The person of whom she is mother is Jesus.
Conversely, if one says that Mary is the Mother of God, one does not necessarily say that she is the Mother of God the Father or God the Holy Spirit. She is only Mother of God the Son.
However, the Church states simply that she is the Mother of God.
This isn't "playing gotcha." This is actually a matter of precision in the use of language, and was critically important in refuting the heresies of Arianism and Nestorianism. Various heresies wished to deny that Jesus was fully God, or wished to separate Jesus the man from Jesus Who is God. By qualifying "God" in Mary, Mother of God, these folks intended to make Jesus [at least a] little less than Who He is.
Thus, the formulation agreed-to by the ancient Church Council, and reiterated unanimously and perenially by the Whole Church was arrived at with great care, to drive home central points of Christology, unambiguously, without wiggle room. The precise language used was very, very important. At least, this was believed nearly universally by the Fathers and the Ecumenical Councils.
But what did they know, right?
sitetest
It is playing "gotcha" when one says "Mary is the Mother of Jesus" and some yahoo replies: "Why do you deny the divinity of Jesus?"
It's unhelpful and it's just playing games.
It makes as much sense to claim they deny the divinity of the Father.
They are only playing on the broadness of the word "God" in a Trinitarian system.