There is very little downside to Argentina from posturing, so why not? The downside only comes if they actually push it all the way to war, and then lose.
I don’t know what the current status of the Argentine armed forces is, but the Brits are much weaker than they were the last time they went to war with Argentina. Argentina has the advantage of proximity, and may feel they have the upper hand.
If Argentina thinks (rightly or wrongly) that they can beat Britain militarily, then this may end in war (or a British retreat prior to war).
If Argentina does NOT think they can beat Great Britain militarily, they may still be able to get what they want through a failure of will on the British part.
Regardless, one thing is clear: The U.S. will not lift a finger to help Great Britain. Obama may even side with Argentina.
He'll probably launch an attack on the Maldives, then wonder why everyone seems confused.