Argentina claims due to some historical technicality that it owns the Falkland Islands. Whether this is true or not is irrelevant: the people of the Falkland Islands have clearly said they want to stay within the United Kingdom. Democracy has spoken, and Latin America has increasingly been recognizing democracy for the past 20 years, so they should respect it here as well.
Britain's claim to the Malvinas is superior to that of Argentina. The residents of the Malvinas should determine for themselves whom they choose to govern their territory. Argentina's claim is based on antiquated notions of divine right to rule based on connection to the Spanish crown. What self-appointed royalty laid claim to hundreds of years ago should not impact the self determination of Malvinas residents.