The UK retains the Falklands because the people living there do not want to be part of Argentina. Besides, Argentina's claim is less strong than Spain's claim to Gibraltar; which they lost to the UK in the War of the Spanish Succession. Additionally, Argentina, having started a war by invading the Falklands and then losing that war has, by international law, lost any claim to the Falklands.
Giving the Falklands to Argentina would be like "giving back" Texas, Calfornia and the whole southwest to Mexico. Should we do that?