If so many Greeks live in Anatolia (modern Turkey), then should we consider Greeks as Asians and not Europeans?

It’s an interesting question—more interesting than people are giving it credit for.

The question I’m going to write on is, how did the balance between Anatolian Greeks and Balkan Greeks change over time, and should that change in geography influence whether we call them European or Asian?

(You might say, it’s only interesting because I’m expanding the question way beyond what OP wrote. No matter.)

Classical Greeks were in both Anatolia and the Balkans. But the Anatolian settlements were regarded as colonies of city-states in the Balkans, so they had less cultural prestige. Moreover, from the perspective of Classical Athens (which is the perspective we all care about the most), Anatolian Greeks were much more overtly under the influence of the Persian Empire (if not ruled by them outright), than Balkan Greeks: another point against their prestige. So, Greeks in the Balkans regarded themselves as “real” Greeks; and “Asiatics” was not a complement.

OTOH, Classical Greeks didn’t call themselves Europeans. They regarded the non-Greeks of Asia as barbarians, and the Greeks of Asia as suspect. But they also regarded the non-Greeks of Europe as barbarians. They’d have no reason to identify with them more.

For Greeks in the Roman Empire, Greekdom was everywhere: Greek was the lingua franca of the Eastern half of the Empire, from Illyria to Arabia. Splitting Europe and Asia as chunks of identity just made no sense back then.

In the middle Byzantine Empire, Anatolia was the heartland, and Hellas, southern Greece, was a hardscrabble province with a bunch of non-Hellenes hanging around, that noone paid any attention too. That’s the time when Anatolian Greekdom had the most cultural prestige among Greek-speakers, and Balkans Greekdom the least. But then too Greeks were no more eager to identify themselves with the Catholic heretics of Western Europe than the Muslim infidels of the Middle East.

Notoriously, Loukas Notaras said in the 1440s, “I would rather see a Turkish turban in the midst of Constantinople than the Latin mitre.” He was talking about his rejection of church union (subjugation by the Vatican) as the price to pay for preventing the Ottoman conquest. It was a very popular opinion. It was also Greeks saying, if our only choices really are European and Asiatic (they regarded themselves as neither), we’ll pick Asiatic.

Constantinople remained the cultural centre of Greekdom until the establishment of the new Greek state. It’s only then that Greeks start to pay attention to the notion of Greeks being European—although there was a lot of pushback to the notion, which lasted for a century.

When do Greeks become proud to identify themselves as European? After the Enlightenment, when the West started looking more attractive than the East; Greek could plausibly say in the 19th century “I would rather be a scissor-arse than wear a turban.” (Scissor-arse, ψαλιδόκωλος, was how Greeks described the Tailcoat.) The precondition to them doing so was that they no longer had the luxury of regarding themselves as neither: they lost that in 1453. And while they were the Rum Millet under the Ottomans, the facts on the ground identified them with Asia, whether they were in Smyrna or Patras.

So the official discourse of the Greek state has been to choose Europe—the West—over Asia. It’s a choice that the remaining intelligentsia in Constantinople did not necessarily approve of: the Greek Orthodox church certainly remained suspicious of the West.

Whether Greeks are Europeans or Asians is a cultural rather than a geographical choice. Every time I walk into a Dewey Decimal System library, I’m reminded that Cyprus is geographically in Asia, not Europe. Greek Cypriots have always been less uptight about being a cross-roads of peoples than Greece Greeks; but you still won’t hear them say “of course we’re in Asia.”

I just wanted to emphasise that, at the time in history when the cultural weight of Greekdom really was in Asia Minor, the choice between Asia and Europe was either irrelevant (we are the Roman Empire, we are neither) or forced on them (we are the Rum Millet of the Ottoman Empire, we are certainly not a bunch of beef-eating Catholics). It wasn’t about which side of the Bosphorus most Greeks lived. And that when they chose Europe after all, it wasn’t a straightforward choice either.

All that debate played out in Balkan Greece, though, decades before the Christian Greek population was extirpated from Anatolia.