Oh you want me to point out how wrong you are? Ouch.
Ok..
The "Roman Empire" fell. I mean, Rome came under the dominion of Germanic warlords. So there was no Roman Empire anymore. This is perfectly clear to people with brains. So the Byzantine Empire could not be the Eastern Roman Empire. Was there continuity with the petty Germanic chieftains ruling over in what is now Italy? Clearly not. So why the bizarre claim to be the Eastern Roman Empire, at this point?
The Bishop of Rome was always back west, so I am not sure why we should care that the patriarch of Constantinople was in the east...at best, he would come in second to the Bishop of Rome for, you know, ECCLESIASTICAL INFLUENCE OVER ROME. This is almost tautological.
What's east Rome? Why apply the name "Rome" to a place entirely separated from Rome, but a long distance, a language, and a culture? All the Byzantines did to maintain continuity with Rome was to retain some of the legal forms they had when they were an administrative division of the Empire. This isn't nothing, but it's surely not everything.
Did the Byzantine Empire not enter a Dark Age? I can't recall much serious scholarship from that time. Jewish, Islamic, and "other" scholarship was fruitful in ARAB-CONTROLLED territory, of course, but the Byzantine Empire wasn't well known for such original scholarship. Take the big names in Jewish and Islamic philosophy - where did they teach?
The utter non sequitur about black people was baffling and insane.