Of course Galtieri started it. But Thatcher had plenty of alternatives other than the military action she took imediately. Even her colleagues in the US tried to persuade her out of it. She needed to get her wavering support behind her. Their actions, the Junta and the Tory's, cost over 900 lives and nearly 2000 casualties for those rocks off Argentina.
No fan of Tories or Thatcher - but that Junta were real Fascists who had murdered 10000+ of their own people by throwing them out of aeroplanes. They wouldnt have thought anything about throwing out a few hundred foreign "invaders" while they were at it - had the British not sent troops in. Callaghan, Wilson, Gaitskill and Blair would probably have done the same as Thatcher - Foot would have probably dispatched a hard-hitting leaflet campaign.
It was certainly a more legitimate intervention (these people were British regardless of what you think of the claim to the islands) compared to Iraq, Libya, Afghanistan, Serbia and so on.