Sorry that you seem extremely offended by this :-D
You want a debate - here...
Great Britain should own the Falklands because if Argentina were to own it, their control would be so bad that another country would come along and take it instead.
Great Britain won the Falklands War, this is how war works, we win - so we own it because that was what the war was about.
Let's face it, if Argentina wanted to take back control of the Falklands, then they would have declared war again already.
If you disagree then the debate begins.