The only people who believe that the Church teaches this are some Protestants.
Even Wikipedia understands this:
Within the Orthodox and Catholic tradition, Mother of God has not been understood, nor been intended to be understood, as referring to Mary as Mother of God from eternity that is, as Mother of God the Father but only with reference to the birth of Jesus, that is, the Incarnation. This limitation in the meaning of Mother of God must be understood by the person employing the term.
The term, Theotokos can be traced as far back as Origen, in 254 A.D.
And really, the term goes all the way back to the New Testament, when Elizabeth refers to Mary as, "the mother of my Lord."
The term is simply a shorthand way of expressing the profound and singular grace of having being chosen to be the Mother of the Man/God, Jesus, with the emphasis being given to Jesus' divine nature. Certainly, her having given birth to a human son would not have been seen as especially significant.
Yeah; we PROTESTants have noticed that they were SO 'insignificant' that Rome denies the FACT that there WERE any!
Which can easily misconstrued by anyone who is not well versed enough in Catholic teaching, including Catholics.
If the church wanted to teach correct doctrine about who Jesus was/is, then the best bet would have been to go back to Scripture (which I realize is almost anathema to Catholic hierarchy) instead of compounding the issue by changing Mary's title.
Because now, instead of simply saying that Jesus is God, here are the Scripture to support it, live with it, the *Church* now has to go into all kinds of convoluted arguments and explanations as to how *Mary, mother of God* really means *Mary, mother of Jesus*, and leaves the thing a bigger mess than in the first place.
*Mother of God* does NOT say the same thing as *mother of Jesus* and if it has to be explained to someone so they don't misunderstand it, then it clearly is saying something different, despite Catholics attempts to deny the obvious.
If it were the right way to address the issue of misunderstanding of Jesus' nature, then no explanation would be necessary.