Greenland is quite far from places like Utqiagvik and Chukotka, where indigenous locals speak entirely different languages. Is it any surprise some people wouldn't want to be labeled that way?

I'll admit "inuit" is pretty widely accepted nowadays, but it's not universally so. The relevant ANLC page gives a good summary of the situation: https://www.uaf.edu/anlc/resources/inuit_or_eskimo.php