Nestorius did not reject Mary's honor; he preferred to call her Christotokos, Christ-bearer, over Theotokos, God-bearer, out of a concern that ran through the whole Antiochene tradition he was trained in. If the divine and human in Christ were united as closely as Theotokos seemed to imply, calling the eternal, impassible God "born" of a human mother risked suggesting that the unchangeable divine nature itself had come into being, suffered and could die, exactly the confusion between the two natures Antiochene Christology existed to prevent. Christotokos, in his reading, kept the language accurate: Mary bore the man Jesus, in whom the divine Word dwelt, without the title forcing a claim about the divine nature's own birth.
The Council of Ephesus in 431 did not accept the distinction and condemned Nestorius's position; Theotokos remained, and remains, the church's title for Mary. But the question Nestorius was actually asking, how to describe a real union of two natures without collapsing either one into the other, did not go away with his condemnation. It shaped the debate that produced Chalcedon's own formula twenty years later, one person in two natures, without confusion, without change, without division, without separation, language that tried to hold Alexandria's unity and Antioch's distinction together at once; and it survives today, largely unmodified, in the dyophysite Christology of the Church of the East, the tradition most directly descended from the Antiochene school's own reading of Christ.