Because it (IMO) better describes what the council was trying to say. Mary being the Mother of God has little to do with Mary, the whole focus was on who Jesus was. Jesus is True God and True Man, and Mary was His mother. So, since Jesus is one person, and Mary is His mother, you can call her Mother (or Bearer) of God. It never meant that Mary was the source of the second person of the Trinity, but that Jesus really was true man and true God from the moment of conception.
But Mary was only the "source" of the 2nd person of the Trinity insofar as He was Man. So why not call her that? Why insist on calling her Mother of God? She didn't give God His beginning. She was mother of Jesus as Man (even while His deity was left intact). The Bible calls her Mother of Jesus. It does not call her Mother of God. This does not in any way take away from Jesus' deity. It does however keep Mary from being put in the potentially misleading position of preexisting Christ as God.
Well stated, thanks for your answer.