"...From the most ancient times the Blessed Virgin has been honored with the title of 'Mother of God,' to whose protection the faithful fly in all their dangers and needs.......".
This one quote from Catechism of the Catholic Church (971) illustrates one of many problems with the title "Mother of God". This strange title, given to Mary by the Catholic Church and its offshoots, is simultaneously a symptom and cause of Marian idolatry.
In one sense, one can see why the term, which is distinct from the more historical "God bearer", might be applied to Mary. She is, after all, the chosen vessel through whom the Word became flesh. Christ being God, Mary carried God in her womb for 9 whole months, bringing Him forth in due time. But is she the "Mother of God", as Catholicism teaches?
There is far too much behind the term "Mother of God". Mothers, of course, are both the originators and respected authorities of their offspring. Thus, the term "Mother of God" gives Mary far too high an honor. Biblically speaking, God preceded Mary. And it's not like God was just a Binity until 2,000 years ago. God has always been triune; there was never a time when God was anything less than Father, Son, and Holy Spirit. Mary is the mother only of His human flesh, making "God bearer" a valid title, since "bearer" has no necessary implications of origins.
To highlight this, consider that Jesus went through many things during His life, including death. Indeed, the death and resurrection of Christ is the central theme of our religion. If Jesus did not die, our faith is in vain (1 Corinthians 15:12-19). Is it accurate, therefore, to call the Romans who nailed Him to a cross "murderers of God"? This term is actually more accurate. The Romans really did arrest, try, beat, and ultimately murder Jesus, who is God in flesh. Yet God did not die. Jesus died, God did not die.
Of course, because of the complex nature of God, particularly regarding the Trinity, this all sounds very confusing. And for good reason; we're talking about God, not some made up nonsense. But although Jesus died, God did not die. You cannot kill God. In much the same way, Mary cannot be the "Mother" of God, because God preceded her, God created her, then God chose her to be the vessel through which He would enter the world in human flesh.
Just as Mary did not create God, she also has no authority over, nor even any greater sway with Him than any other human being. In Roman pagan religions, the gods genuinely did have relatively mundane origins. Juno, for example, was the mother of Vulcan. But in Christianity, God has always existed, and has never been dependent upon, nor submissive to, any other power. This is why, contrary to the assertions of the Catholic Church, the faithful do not fly to Mary's protection in all our dangers or needs!
This is, by far, the most dangerous implication of the title "Mother of God". Mothers are more than just originators. They are well respected authorities. Our mothers can tell us what to do. They can make requests of us that we are more likely to honor than requests from others. Thus, "Mother of God" can strongly support Catholicism's assertion that Mary can intercede with God on our behalf.
But what does the word of God tell us? "For there is one God and one Mediator between God and men, the Man Christ Jesus, who gave Himself a ransom for all, to be testified in due time,". There is one mediator between God and men. Who is that mediator? The Man, Jesus Christ. So how many Mediatrixes are there? Zero. Is Mary the one mediator between man and God? No.
And so you see the problem with the title "Mother of God". It is a fallacious title, ascribing far too many false attributes to a finite creature. Though faithful, and certainly blessed among women, Mary is not the "Mother of God", nor does she have basically any of the divine attributes ascribed to her by the apostate Church of the "murderers of God."