I still don't see how that's remotely relevant. I was using it in the context of explaining who lived in Greenland, in contrast with Indians and Europeans. "Eskimo" is the maximally broad term which makes this distinction, as I pointed out in the conversation. It's also the more familiar term.
When it comes to the inhabitants of Greenland, I generally use the term "Greenlander," however for people who don't know who already live in Greenland that's uninformative. When it comes to the Inuit of Canada I generally use the term "Inuit," but there are contexts where "Eskimo" makes sense as well.
This doesn't make sense, when the Inuit of Canada and Greenland have made it clear that they don't wish to be called Eskimo, to the point where it's been removed from all official documentation in those countries as a result of their stated preference as a group in those regions. When you refer to Greenlander natives, the term Inuit is perfectly acceptable, and I don't buy the idea that you have to use Eskimo as a "maximally broad" term when it's factually inaccurate in the first place as the people you're identifying with that term don't use it and have stated they don't want to be identified with it.
It's also absurd to use the status of the native people of Alaska to justify sloppy usage of broad terminology, and omit the context that you were at that time talking about the people of Greenland. What Native Alaskans wish to be called has no bearing on the intentions and feelings of the people of Greenland.