As settled as the Arian controversy was, now people had too much time to think about just how Jesus is both God and man.
Apollinarius taught that Christ's true body and soul were at some point replaced with the logos. This emphasized his deity over his humanity, and also made Christ sound like he was possessed at some point in his ministry. Constantinople condemned that thought in 381.
Then Nestorius decided he did not like calling Mary theotokos, or God-bearer, because it exalted her too much. He preferred Christotokos to say that Mary only bore his human body. Earle Cairns says that in "Siamese twin fashion", Christ's perfect humanity was only mingled with God. This made him another Arian demigod, not God in the flesh. This was clearly wrong. Cyril of Alexandria condemned his doctrine at Ephesus in 431. Sadly, his Christology is what the Asians still believe.
At the Council of Chalcedon, the Church officially proclaimed that Christ was "complete in Godhead and complete in manhood, truly God and truly man, two natures without confusion, without change, without division, without separation." Jesus was completely God and man at the same time, not a Ninja Turtle on the half-shell.
The people kept using Theotokos to describe Mary simply because the child that she bore happened to be God the Son. Since all Christians host the Holy Spirit in their souls, we are all theotokos. We all bear God as he guides us through our lives and to our salvation.