They're still butthurt over the Falklands War. Maybe it's their opportunity to invade again.
I don't get why Argentina even cares about the Falkland Islands, even if the Spanish claimed it (as they did many other island that fell into British and French rule) it wasn't settled until then and the people who live don't mind British rule. Maybe unless there's oil ridges around it, but I don't know.
What's also interesting about Argentina is the fact that they also have a lot of Welsh and Irish settlers there.