The British own them and should own them.
The people who live there do not want to be Argentine. Argentina only had them for
15 years back in the early 1800s.
If the European colonists who live in what they call "Argentina" decide to give back their land to the Native Americans(most of whom they have conveniently eradicated through the centuries), then maybe Britain might consider it. And pigs will fly.
There will not be a second Falklands war and the Trident submarine(s) cruising silently around in the south atlantic packing the 'heat of a million suns', as Kim Jong-Il says, will ensure that.