I remember a couple of years ago an explanation of something along these lines. Those who had an issue with Jesus' divinity found themselves in the Arian camp. Those who had an issue with Jesus' humanity tended to go to one of two extremes. The Nestorians treated Jesus divinity as having little to do with his humanity and vice versa, so you'd have a strange expression like, "Jesus the man died on the cross, but not the Jesus the divine." The monophysites swallowed up his divinity so that it was fused into a singular (mostly) divine nature. Again, at the expense of the humanity of Jesus. Even now, occasionally on the bulletin boards, "Chalcedonian" Christians will see expressions like "the humanity of Jesus" or "Jesus the Man" and think that it was some sort of intrinsic denial of his divine nature or Arianism in disguise. Why was the humanity of Jesus - or rather - that Jesus could be simultaneously truly human and truly divine - so problematic?
Cyrillian Miaphysitism seems like a milder form of monophysitism, and I read that some have tried to make it compatible with Chalcedonian expressions. Forgive me for saying this, but it seems similar to the semantics involved in making Western and Eastern approachs to the Trinity to unambiguously mean the same things, without in any sense departing from the Western terminologies. So from Latin/Greek semantics it's Syrian/Greek semantics. I suppose if you can get both confessions to assert the same thing (though semantically worded differently) you'd have unity, right?