Even if we are somehow made to concede possession of the islands can the Falklands not just declare independence as a sovereign state?
They could do, technically, but could they make it stick? 2900 people is a rather small population for a country.
why do Argentina believe they have a right to it?
I'm not even sure that they do. It's a political tool and attempted resource grab, so the Argentinian government would be doing it whether or not they believe they have a legit claim.
1764: A tiny French colony claims one of the islands for France.
1765: A tiny British colony claims all of the islands for Britain, apparently unaware of the French colony on a different island.
1767: France gives its colony to Spain and withdraws its claim to that 1 island.
Both the British and the Spanish colonies were abandoned a bit later, but neither country withdrew its claims. Argentina didn't even exist at this point.
Britain returned with a better funded colony. Spain never returned. Argentina never had a colony or anything else on the Falklands.
So when Britian returned permanently in 1833, the islands were uninhabited.
The basis for the Argentinian claim is that Argentina inherited the Spanish claim and Spain inherited the French claim, therefore the Argentinian claim is backdated to the French claim even though Argentina didn't exist at that time. It's unclear whether or not that would be legal and the French claim was only to 1 of the islands anyway. It was also never supported and it was withdrawn when France abandoned their colony.
The Argentinian claim is dubious at best, which is why it relies so strongly on disinformation such as talking about the UK giving the islands
back to Argentina, which implies that they used to be Argentinian. That's completely false - they have never been Argentinian.
