Ultimately though, Argentina could easily have gained the Falklands back in the 1980s but chose to create the circumstances whereby invading meant that there is no realistic way these discussions will ever occur.
Having met Falklanders and heard about the way they were treated by the Argentines during the invasion, they have no desire to ever be Argentinean. The way to make the Falklands want to be Argentine is to love bomb them, not make them out to be nasty little colonialists.
The UK will talk to Argentina the day the Falkand Islanders ask them to do so - until Argentina stops clinging to a very odd and inaccurate account of history, comes to terms with the reality that whatever may or may not have happened early in the 19th century is utterly irrelevant in the early 21st century, and tries to find a way to work with the Islands, and not cling to them as some kind of mascot or charm, then this will continue to be a running sore.
The problem is Argentinas to solve - treating the Islanders like idiots, not potential countrymen is not the way to do it.