There are fewer than 4000 people living on the islands.
When there was a referendum about whether to keep the current association with the UK, 3, three people voted no.
One, who cares about a tiny amount of land and a few thousand people, it should not be a big international issue.
Two, self determination of a population should be important. When 99.8% of the population votes for keeping the status quo, maybe just let them.
The British didn’t actually care that much about the Falklands - the British government had spent most of the 1970s trying to give them to Argentina, but the islanders opposed it, and they stirred up opinion against it in the UK and in Parliament, and the government’s plans were stymied. But when Argentina attacked-if the UK didn’t fight back, it would be open season on all their other territories around the world, including others they were less willing to cede. And the war destroyed all political prospects of the UK public ever agreeing to support a peaceful transfer.