the names and boundaries of continents are arbitrary and don't matter. that said, the most common definition, really more of a vibe, of a continent is size. Europe is 3 times larger than India. It's twice as large as India, Pakistan, Bangladesh, Sri Lanka, Nepal, Bhutan, and Afghanistan combined.
There's way more tectonic plates than continents and a lot of landmasses we think of as contiguous are on different plates. Itd be very impractical to try to make them the same. Iceland would be a transcontinental country, California would be its own continent, Asia would be several continents, there would be continents that are just patches of the Pacific Ocean or the Caribbean, and so on
I don't think Europe or the West as a geopolitical force is the same as the continent. There are other areas that are unambiguously in Europe that aren't part of "Europe" similarly to how Russia isn't. Are Belarus, Bosnia, Serbia, or Moldova really part of the club the way France and Germany are? Of course not. Greece or Hungary arguably aren't either.
not gonna argue that, greece relative to europe occupies the position of peurto rico relative to the US.
I just think that the self-concept of europe is chauvinist and it's more of desired boundary than anything real, and calling it 'a continent' gives it legitimacy that it does not deserve.
they made the definitions before they'd invented white people though. IIRC this nomenclature comes from the ancient greeks. it's very ancient european cope.