As an occasional "Nestorian" blog, and certainly a pro-east-Syriac blog, I have some interest in that history. Matt Crawford traces the history to Nestorius' roots in Antioch. Good luck to Crawford; I hope he fares better than some others.
Cyril is meanwhile (somewhat) rehabilitated as not just making up theotokos (Latin, deipara) himself. Most people (like me, and Candida Moss) have seen Cyril as a base opportunist. We here have inherited Schwartz in 1928. Even if, of late, we have had to back off some of the Agora slanders against this Miaphysite saint.
Emperor Julian, born to Christian (Eunomian!) emperors, among his Christian foils had to address such as were saying theotokos or something like that. As a pagan, he recognised this term as pagan, like a mortal-ess birthing Heracles or Dionysus. The Eunomians weren't saying this; only a Miaphysite could say this. So Cyril was heir to a Miaphysite tradition. Gregory of Nazianzus knew this as of Apollinaris; later authors would see Eutychianism or "Julianism". Nevertheless Gregory (somehow) affirms theotokos.
Nestorius (and, I could add, John Chrysostom before him; and Diodore of Tarsus) grew up where Apollinarianism was staking its last redoubt. Theotokos could be tolerated anywhere else. Not in Antioch, says Crawford.
My reading of Crawford suggests he personally supports theotokos, or at least some form of Christian unity without taking that seriously. He wants to humanise Nestorius without accepting him. Maybe he can. I'll leave that aside for now.
The story may start with Paul of Samosata, all the way back in the middle 200s AD. He had posed, perhaps clumsily: for the Word is from above; Jesus Christ, a human being, is from here
. The Council of Antioch shut him off AD 268. Eunomian subordinatism owes to this thought - if taking Paul's words literally. Athanasius devoted at least half his career against Eunomianism, maybe more than half. Nestorius' dyophysic might descend from Paul, also; but I think it turned out better, and I don't know how far Athanasius would have disliked Nestorius.
Gregory and (maybe) Athanasius could have threaded this needle. Real problems started emerging out West. Not the problems I'd expect.
One Leporius of Marseilles had propounded a notion of Christ as the merger of God and man. We don't really have the exact words he said, but the Masillians booted him out. Leporius then met Augustine in Africa and, basically, did the apology tour. The ensuing libellius survives through extensive quoting by John Cassian who brought it back to Gaul, with Augustine's personal imprimatur (if mostly an antiPelagian text, here). Cassian's aim was to rebut "Nestorians" who may well have preserved Leporius' earlier work.
Crawford carries over recent scholarship on Cyril's oeuvre, also: On the Incarnation of the Only-Begotten and that There is One Christ and Lord according to the Scriptures. This - for De Durand - preceded the whole feud with Nestorius. Nestorius' accession as the Patriarch of Constantinople, for Crawford, was unlucky for Nestorius, because Cyril was already an enemy of the dyophysitism who also shared his antiApollinarian credentials (or so he claimed).
I admit, I think Leporius got it right first-time. Augustine was always a momma's-boy who could easily have fallen in with the Ephesus councils, had he been born that late. I like to think - say - Jerome would have known better, hence why his work got translated to Syriac and passed East.