Las Malvinas / the F**kland Islands are such a barren wasteland that most things of any worth have to be flown in or sent by sea. So there is zero chance of the place being able to support major oil industry requirements - and don't forget that both the islanders and woolly-hatted busy-body envirofundamentalists would be up in arms if the seals / penguins or other wildlife were to be forced to move out so that oil installations could be built on the islands.
I seem to remember that the Shetland Islands were considered an environmental paradise at one time, then along came oil. The elders of the Shetlands proceeded to negotiate themselves some excellent terms and conditions and all environmental issues were 'overcome'!
Das Island, in the Arabian/Persian Gulf can only be supplied by sea or air and has been for the last fifty years, providing major oil field support.
I'm just amazed that Argentina tore up the agreement on oil, talk about self destruct!