I disagree with the comment that it was pointless. These islands, inhabited only by British subjects, were wrongfully taken. A corrupt government was humbled and forced to give up power. Britain proved again the valor and skill of its royal marines, SAS, and other units mentioned in this article.
Why was it pointless ?
The Argentine invasion, which precipitated the war, was pointless. Argentina had no particular use for the islands. Why cause a war in order to control a bunch of sheep and some more-British-than-the-British ex-pats who certainly didn't want to become Argentinian? What good did it do Argentina?
It is certainly true that the British involvement in the war was more reasonable than that of the Argentinians. The British fought to repel an invader and on behalf of people who wanted to remain as they were. All the same, it is hard to justify overall, in my opinion. It is true that the inhabitants should have been allowed to remain subjects of whichever country they wanted. But about a thousand people died in order for this to happen. Was the right of the Falklanders to be British rather than Argentinian more important than those lives? I can't see that it was. A just cause does not necessarily translate to a just war.
As for "proving the valour and skill" of the British forces, I hardly think that's a reasonable justification for anything.
The war also stirred up appalling and now-notorious jingoism in Britain; think of the infamous "Gotcha!" with which the Sun greeted the attack on the Belgrano, or Thatcher's outrage when the archbishop of Canterbury proposed to pray for Argentinians who had died in the war. Thatcher's own jingoism was obviously incompatible with regarding enemy soldiers as human beings or worthy of a second thought. Finally, the war was a key factor in Thatcher's re-election in 1983 - not a desirable consequence.