What I know: The council declares Christ perfect in divinity and perfect in humanity, the same truly God and truly man. Fair enough.
Now we have Monophysites who think that Christ is purely God, they break away and I get why. Then we have Dyophysites who appear to think Christ is half and half, I see why they are pissed too.
But the Miaphysites? They believe 'Jesus's humanity and divinity were of one in superable nature'. This seems like exactly what the council of 451 had just said.
Please, if you are a historian of theology or church history or have more subtle knowledge regarding the background to this split please enlighten me; I'm sure I'm missing something. All replies appreciated.
Monophysites and Miaphysites refer to the same group - one is just a preferred name. They are all trying to follow St. Cyril of Alexandria who, thinking he was quoting St. Athanasius (but actually quoting Apollinaris), talked about the μία φύσις τοῦ θεοῦ λόγου σεσαρκωμένη (one incarnate nature of God the word).
Nestorius, the Patriarch of Constantinople between 428 and 431 (who was deposed at the Council of Ephesus) had posited a pretty strict split between the natures of Jesus such that he ended up creating two subjects of predication in Jesus. His famous Sermo 9 (found in Loofs' Nestoriana) is the easiest place to find this. He is so worried about protecting divine impassibility that he ends up attributing miracles to Jesus' divine nature and suffering to His human nature. The problem is that you no longer have a single subject of predication (a person), but two subjects of predication (natures) who are somehow related to one another (I say "somehow" because figuring out what Nestorius meant is a mess, to be honest).
So after Chalcedon, you get followers of Cyril, who wrote against Nestorius, who think that the Chalcedonian definition is Nestorian because it teaches two natures. They stick with an overly literal understanding of Cyril's phrase (which is incorrect - cf. Hans van Loon's The Dyophysite Christology of Cyril of Alexandria).
The conciliar definitions that come out of Ephesus (431) and Chalcedon (451) agree in part with both Nestorians and Miaphysites. With respect to the former, conciliar Christology agrees in dyophysitism (i.e. the belief that Jesus has two natures and has them in their fullness), but disagrees with Nestorians on the unity of Jesus' person. With respect to the Miaphysites, the councils agreed on the unity of person (there's only one "I" in Jesus), but disagreed on what seemed to be a confusion or mixing of the natures (such that divinity becomes humanity or vice versa - which is unacceptable to anyone who wants to preserve divine impassibility, among whom we can number Cyril of Alexandria).