Argentina has claimed sovereignty over the Falklands due to the islands being in close proximity to the the Argentinean coast line. Just because the land is near them, it does not mean it is theirs. A good example of this is the Uk and Ireland. Ireland is very close to the UK, yet the UK has not claimed sovereignty over it. The only right they could possibly have over the Falklands is if the falklands islanders wanted to be governed by Argentina and not the UK, and obviously, this is not the case. The islanders wanted to remain under British control, giving Britain more rights over the Falklands than Argentina.