I didn't know the detailed background before I actually visited the place. I'm personally disinclined to support the actions of the British Empire and the various colonial adventures that absolutely destroyed so many countries and cultures. I am a very strong supporter of the Chagos Islanders. My instinctive reaction to the Falklands was essentially "the Brits are at it again", as the Irish say.
However, I visited. It's a bit like visiting rural New Zealand I think, certainly as far as the sheep and the accents are concerned. It was nice to be able to open my purse and spend normal money rather than wonder whether this place takes Euros or maybe US dollars? (And they didn't bat an eyelid at Scottish notes, which was just as well.) There are a few people who are rabid Union Jack wavers, but this is not most people. The people I spoke to told about how proud they were to be self-sufficient, but at the same time how grateful they were that Britain was prepared to defend the islands militarily. Of course they wouldn't need that defence if Argentina wasn't circling like a shark.
They've been there for at least four generations. It's their home. They farm the land and they work to improve their infrastructure. They're developing their tourist trade. Many of them have never been anywhere else.
Since then I have discussed the issue with an Argentinian acquaintance and while it's obvious Argentinians feel strongly about it their actual claim seems to be entirely based on "the islands are nearer to us than to anywhere else" and "we had a small military garrison there a couple of hundred years or so". It's not compelling.
It may be that the current population was put there as a "plantation" to secure that area of the south Atlantic for the British Empire, but that was a long time ago. Now, it's just another place that has a population of European-origin settlers who have made it their home (not unlike Argentina itself), and very unusually they haven't displaced anyone else to do that.
It's possible that interests as regards control of local resources might arise to cause conflict in the future. If a lot of oil was found near the islands, that could get interesting. But at the moment it's just people, on a fairly small bit of real estate, that Argentina which has plenty of real estate of its own wants to put its name on for reasons that seem no more than nationalistic pride.