For historical purposes I would like to point out about the Argentinian claims over the Falklands/Malvinas islands..
Before 1810 those islands were included into the Sudamerican territories controlled by the Spanish crown.
After the Argentinian independence war with Spain those islands were under Argetinian government control.
In fact, the Argentina had positive control of the islands from 1820 until 1833 when the British government took the islands shipping the Argentinian people back to the continent (there was not self determination...).
Six month after, there was a rebelion initiated by two Argentinian "cowboys" and 5 other Charruas. They were commanded by el Gaucho Rivero, who killed the British governor.
The UK took over again after 5 month, during that period the Argentina was in a civil war between Buenos Aires and the rest of the country.
So, it is not true that those islands have never being Argentinian...