Without wishing to get too bogged down with a topic that has been aired to death, France and Spain have a greater claim to the islands than Argentina having both occupied them prior to Britain’s first proper spell which began in 1771 (although a British exploratory force had landed there as early as 1690).
The idea that sovereignty could be transferred to Argentina upon its independence from Spain (which was achieved between 1816 and 1825 depending on whose version of events is believed) is somewhat fanciful. It was not even clear that Spain still had a claim to the islands at that time having shown little interest in them since their departure in 1811.
The notion that Argentina can now suggest that the matter of self-determination is somehow irrelevant because of claims that are, at best, of dubious merit and are in any case 200 years old demonstrates adequately the attitude of Argentina towards the current inhabitants. In essence they are implying that something that happened the best part of 200 years ago overrides the wishes of people settled there now.
However, we are where we are and harping on about two centuries of disputed claims will not help. But I’m a bit alarmed about Mikey’s suggestion that we should “Just ignore them and it will go away, just like it always does…” It does not always go away as events of 1982 clearly demonstrated. Should Argentina decide to repeat their actions of 1982 today there is no doubt that the UK lacks the ability to mount a recovery expedition (although the islands are considerably better defended than they were then). I‘m also fairly sure that the UK lacks the political will to have a re-run of 1982. The only saving grace is that Argentina has not fared too well in either respect in the last thirty years either.