Digging up the logic from the Third Ecumenical Council of Ephesus in 431:
-Christ is 100% God, 100% Man in the same body.
-Mary brought Christ into the world, in other words, gave birth to Christ.
-Christ is God, thus Mary gave birth to God.
-Final Analysis: Mary is the Theotokos (the God-bearer)
The part where Nestorius messed up, was the first part. Because he did not want to call Mary the Theokos, he concluded that she only brought Christ's humanity into the world and then concluded that Christ was in two separate bodies: God and man. (or something similar to that).
The part that many Protestants leave out from this Council, is that Mary is to be called the Theotokos. While some may acknowledge the Christ supposedly being two separate beings, they still forget the Theotokos part.
To say that Mary did not give birth to God, is to say that she did not bring God into the world, which is the same as saying that Christ was two separate beings. Granted, she did not give birth to the Trinity (which is something sometimes misunderstood) she did bring Christ into the world who is God.