Nestorius was the first to object to the term in the first half of the fifth century, also misunderstanding the term to suggest that Mary was the origin of God.
Some today object to the phrase because they believe it is a Catholic teaching.
But it must be realized that the phrase is not only accepted by Catholics, but by Protestants also. This, however, is a pietistic approach to the term, not a theological. The theological necessity of saying that Mary was the mother of God is to affirm that the baby she gave birth to was not only man, but also God. We cannot speak of His humanity or His deity in isolation, but must always speak of them together in unity. Whatever can be said of one of His natures can be said of His whole person.