The big difference is the falkland islands are populated by brits loyal to britain whereas Greenland is populated by greenlanders who hate denmark because the danes committed many acts of genocide against greenlanders.
> I think most Americans are much more mobile and not used to the idea that someone could be strongly attached to an area as their home.
You think the people in the falklands are "native" to the falkland islands?
There are people who have been born and brought up in the Falkland Islands and have connections going back generations. They have been there longer than anyone else, and the islands had no previous indigenous population before France first colonised them.
As to whether they are native, that is a whole other can of worms, but they are more rooted to there than people who live in continental South America. Geographically they can't claim to be British but by sympathy they are. Things were shifting in Argentina's favour until the invasion.
By the way, this does apply to a certain percentage of Greenlanders. There are a few European Greenlanders, or people of recent mixed heritage so we could make similar arguments about them.
> I think most Americans are much more mobile and not used to the idea that someone could be strongly attached to an area as their home.
You think the people in the falklands are "native" to the falkland islands?