How does the reason behind the schism make the west more prone to further division and the east more prone to want to be holy as He is holy?
At least in part, having hierarchs who were essentially secular rulers created a mindset in the West which was and is antithetical to that in the East where there has always been, at least until very recently, a society ruled by an emperor of one sort or another. The Church didn't need to rule. In a system like that, Christians from patriarchs on down can embrace the concept of dying to the self so that the eye of the soul, the nous, becomes clear and man can experience the uncreated energies of God. Creation is transformed, returning in however small a scale, to its pre Fall state and we reach a state of theosis.
The Western pyramidal hierarchy prevented this one the one hand, and gave birth to the Protestant Reformation on the other.