The problem is not what the islanders want or want not. The islanders can and surely would remain british citizens, their way of living and government would be respected, their tax policy should and could have a special status, no mandatory educational or religious imposition would be put upon them... simply because they are not the issue.
and why exactly would anyone trust a country that 'disappeared' almost 30.000 of its own people in very recent history.
The Argentine economy has been rocky for many years and its politics are complicated and divisive - I have relatives (Argentine nationals) who moved out of Argentina because the country is so unstable.
All the Falklands mean to Argentina is money and the saving of face (that is where the Latin mentality has its flaw).
I believe there is an island in the River Plate that used to belong to Uruguay until Argentina bullied them out of it in exchange for a less important one further up the river - perhaps they could give that back before demanding the return of the Falklands.