What people created the notion of Europe? Ancient Greeks.
Where did the Ancient Greeks live? On the border between Asia and Europe.
The Ancient Greeks had not circumnavigated the Arctic (and they didn’t believe a word Pytheas said). The Ancient Greeks did not know anything about the Urals. The Ancient Greeks did not even know what a continent was.
All they knew was, there was stuff to the East of them, stuff to the South of them, and stuff to the Northwest of them. They called each a different name. And to them, the Aegean Sea (and I guess the Black Sea) were as big a divider of landmass as the Mediterranean is. Remember: they did not know about the Urals. And they wouldn’t really have cared.
So the notion of Europe and Asia predates modern notions of continents, and made sense to a people living where they did. The notion was perpetuated, because European culture was defined by what the Greeks thought.