St. Cyril of Alexandria's story comes from Martin Chemnitz's Loci Theologici written from 1554-1584. This translation is by J.A.O. Preus, published by Concordia Publishing House, St. Louis, © 1989, pp. 114-115.
Now, it is said that this happened: Nestorius had as a presbyter a certain Anastasius, a man like himself and one whom he therefore loved. This man had said in a sermon on several occasions (perhaps not having sufficiently considered the matter) that Mary is not to be called the mother of God, as all antiquity called her, but the bearer of man. Bishop Nestorius was appealed to about this matter, to compel his presbyter to retract the statement which he had spoken either in carelessness or dangerously. But Nestorius did not want to desert Anastasius, whom he favored. He therefore shamelessly began to argue, out of a love of controversy, in defense of this proposition, and as it happens in such disputes, when strange notions are defended, the matter proceeded to the point that Nestorius denied that God was born, suffered, was crucified, etc. but said that only the man born of Mary suffered and was crucified and that God was present with the man just as He is present with one of the saints. For so he repeatedly said as a proverb, as it were: “Do not glory, Judas, because you have not crucified God but a man.”
When Cyril of Alexandria saw this fire springing up in the royal city from where the flame, fed with fuel, could spread widely and the whole truth of the church be destroyed, he wrote to Nestorius, admonishing him to [put] better thought to the matter, and he pointed out that with the fountains of trouble opened, what great ruin to major articles of the faith this dispute would bring with it. But when, from the invectives and blasphemies with which Nestorius responded, Cyril saw that there was no hope of improvement, he called a provincial council at Alexandria and also wrote to the western churches. But Nestorius at the royal court in the meantime had obtained an imperial rescript of the ruler in which Theodosius sharply rebukes Cyril because he had stirred up such commotion against Nestorius without demanding an investigation by the church of Constantinople. Among other things Theodosius said, “We will not permit that both the cities and the churches e disturbed.” [Cyril] was also criticized in the Sixth Epistle by the clergy, because he had too strenuously stirred up controversy against Nestorius.
But Cyril, burning with the zeal of the house of God, was not disturbed by those clamors, but wrote to Theodosius and to the royal sisters of the emperor books on the true faith, which are extant, in which he showed with how great blasphemies and errors the view of Nestorius abounded. And since the matter pertains to the whole church, he asked that there be an inquiry in a universal council, for the calling of which the authority of the emperor was required. The emperor called a general council at Ephesus [431] A.D. And on June 20 [actions prior to the opening] began, when, after Cyril had set forth his conviction that there is not one Son who was born of the Father before all worlds and another Son who was born of the Virgin Mary, Nestorius rose and said, “I will never confess faith in a God who is two or three months old. Therefore I will no longer come to meet with you.” Therefore, since he would not appear, though he was often called, when his writings had been read, he was condemned by lawful decision of the council.
But John of Antioch, who arrived three days after the condemnation of Nestorius, moved by a certain ambition, became angry at Cyril because he had taken so much on himself that he condemned Nestorius without the expected preceding arrival of the Bishop of Antioch. Therefore out of hatred and with love of controversy he took the side of Nestorius and in turn condemned Cyril.
Also Theodoret, the bishop of Cyrus [in Syria] who was called “the wise” because of his great learning, wrote against the Anathemas of Cyril and in favor of Nestorius. Cyril very learnedly refuted this writing, as can be seen in the fourth volume of Cyril’s works.
Therefore the emperor, aware of the dissension of the bishops, did not want to consider the condemnation of Nestorius settled; and the eastern [bishops] took Nestorius away with them and took respectful care of him for four years in a certain small dwelling near Antioch. But John of Antioch, finally fearing the judgment of God, when he saw that many were infected with that pernicious notion of Nestorius, wrote to the emperor who by the imposition of his official authority brought about a reconciliation between John and Cyril. But the emperor ordered Nestorius to be sent into exile. While in exile, Nestorius indeed pretended to recant, saying, “Mary should also be called the Mother of God, and let the sad contentions come to an end.” But because he still held on to basics of heresy, he was again deposed into exile. Now, it is written that his life in exile was most miserable, and people even say that he was swallowed up by a hole in the earth. But Evagrius testifies that before his death his tongue was eaten by worms. The rest of the story is copiously set forth in the Trip. Hist. and in Nicephorus.
Again, although a knowledge of the account is useful, yet it is more necessary to know what his teachings were, against which doctrine of the communication of attributes was later very carefully set forth. For it was not a controversy about the veneration of the Virgin Mary when the question was debated whether she was to be called the Mother of God, but about the doctrine of the incarnation of the Son of God.
It is commonly said that Nestorius taught that in the incarnate Christ there are two persons, just as there are two natures. But this must not be understood as if Nestorius was so crass as to believe that in Christ there are two persons, just as I and you are two persons. For he himself says in his confession that Christ is one. “Perish all suspicion of a duality of Sons and Lords!”
But this was his error, as is evident from the Council of Ephesus and from Cyril: Those terms which are predicated of Christ in Scripture he divided like this: He said that some applied to the man Christ, some to Christ as God. For he said that the man Christ is born but not God. For it is written, “I am God, and I do not change” [Mal. 3:6]. And he said that God was present with the man Christ when He was born, in the same way that the Holy Spirit was present with John the Baptizer when he was born. For in the womb of his mother he was filled with the Holy Spirit [Like 1:41], and yet the Holy Spirit was not therefore said to be born. So also in other things. He said that also those words, “Let this cup pass from Me” [Matt. 26:39], were unworthy of God the Word. Likewise, “My God, My God, why have you forsaken Me?” [Matt. 27:46]. On this basis he posited two persons in Christ, because he attributed some actions to the man Christ, others to the Christ as God, whereas the actions are to be attributed not to the natures but to the persons.
Therefore Nestorius totally denied the communication of attributes. He indeed confessed that Christ was born of a virgin, but because He was born according to the humanity, not according to the Deity, which was from eternity, therefore he said that Mary had given birth only to a man, not to God. This is almost the same as saying that Elizabeth gave birth to John the Baptizer according to the body, not according to the soul, and therefore she is not the mother of John the Baptizer.