People identifying themselves as European? That's still rather a strange thing to do for anyone. Only a few people who are seriously supportive of the EU would do that. Most others would either identify mostly by their national identity or even by a regional identity, like Scottish, Catalan or Occitan.

And if one would connect to a larger entity, most people would see little reason to then limit themselves to 'European'. People might call themselves "world citizen" to emphasize their international outlook, or "Western" to emphasize their economic and political privilege. This is partially a remnant from the Cold War, in which Western Europeans tended to see themselves as part of the NATO block more than as part of the EU, for better or for worse. It's possible that in the former Warsaw pact states the self-identification as European is easier nowadays, I don't know.

So is there resistance to self-identifying as European? Yes, almost everywhere in Europe this resistance exists. People are anxious to retain some significance in their national or regional identities, as small as the importance of their governments might be to their daily lives. Although most Europeans are reasonably accepting of their European neighbours, and in practice quite supportive of European cooperation, a large part of the European population is very resistant to Europe as an idea. Self-identifying as European would need to overcome that resistance.

And frankly while I personally am quite in favor of further European integration, I would rarely if ever self-identify as European. It just rarely seems relevant.

Question to OP: are you referring here specifically Europeans as in EU member states or a wider european identity?