And uniquely for back then, they believed that their role was a universal civilizing one rather than a particular one - which leads me to my second reason: Rome had a genius for making outsiders into Roman insiders. Wherever Rome went it implemented its distinctive package of institutions and cultural artifacts, elevating the local elites culturally and legally to become Romans. In doing so, newly conquered peoples were in due time turned into pacified provinces of the Roman Imperium. That the eastern half of the empire spoke Greek really didn't matter: it was still Roman rule with the same norms. And the same pride and cultural "autorictus" that both overawed and rewarded other elites. And the outcome? Prosperity, peace and hegemony unrivaled in its scope and length until the modern era.
It seems a religious madness has gotten hold of our educated and wealthy elites so that they cannot see our strengths or others' deadly, contagious weaknesses. Which is a terrifying portent for the future.