Fair comment, but as I understand it, the Falklands and South Georgia were uninhabited 200 years ago, all that was there were colonies of penguins and seabirds. The Argentinians had no interest in the islands then because they were desolate windswept hell holes that no one wanted to live on , otherwise they would have colonised them before we got there. The only reason we colonised them was because they made good bases for the Whaling industry. The Argentinian claim only came about after we had spent money on them making them inhabitable and no doubt the lure of the oil and gas is what is really driving them on again.
The Channel Islands are a few miles off the French Coast, therefore the French should claim them if you go by the Argentinian way of thinking. Sensibly, the French don't see it that way and understand they are British.