Almost three centuries since Christ was crucified and resurrected, a series of Christological debate had started to surface trying to find an explanation in order to explain the status of Jesus, both his divine nature and his human nature. As colourful as the senate in the early Rome Republic, this series of debate were often motivated by differences, may it be political, cultural or biblical.
Politically, the Roman Empire was in its decline and for the Christians they have just stepped out of a very dark era of non-violent suppression from the emperor Julian. As Julian was killed in battle, under 'new management', the empire once again divided into east and west and Christians regain their privileges that were taken by Julian and their social status being restored. Eager to retain control of the influential Christians, the emperor maintain the customs of calling councils in order to stabilise his internal affairs. As a result, Christians and the emperor are now in a game of politics where both side has a substantial influence upon the other, emperor can call a council to internalise any biblical dispute before it spill out on the street, and Christians can now hold the emperor for ransom if the emperor made an unpopular decision, as in the case of the exile of Nestorius.
The culturally diverse empire was divided into two parts, East and West, and because of the cultural divide and the difficulty of travel and communication, these two part essentially operated like two separate empires, both in political and in the church level. That means misunderstanding was inevitable since understanding was barely existed.
It also would not take long for difference of opinion to emerge on the view of the Bible, the two different schools of thought - Alexandrian (neo-platonic: emphasised on divinity) and Antiochene (Aristotelian: emphasised on the two 'natures' of Christ) provided two different views onto the Christological debate based on their philosophical viewpoint of the material and the spiritual.
The Christological debate started around 375 AD when Apollonarius described Jesus has the body of man and spirit and will of the Logos. This caused much controversy around the Alexandrian scholars, because it separates the flesh and the Logos, meaning while Jesus was on Earth, he was not truly divine inside out. Which may suggest Jesus was homoi-ousias while he appeared as a man, not homo-ousias. The debate continued while Nestorius spoke of the distinctness of body and Logos, Cyril went the opposite saying the divine permeate out of the body. This led to the first council of Ephesus in 431 AD, which led to the minor exile of Nestorius, Cyril being labelled "monster, born and educated for the destruction of the church" and the major schism - formation of the Assyrian Church of the East.
The Biblical differences goes beyond the Council of Chalcedon, which the council first repudiated the Second Council of Ephesus while trying to walk the middle path between the two schools of theology produced a "Definition of Faith" declared that in Christ there are "two natures in one person". The Council's findings were rejected by many of the Christians on the fringes of the Byzantine Empire, including Egyptians, Syrians, Armenians, and others.