Wensleydale is correct - big difference between trying to regain your own territory and attacking another country
We never went to war with Argentina in a legal sense - it was more a "police action"
Plus our American allies would have been really p***** off and it wouldn't have done much with the other S American nations who were either on our side (Chile) or neutral-ish (Brazil)
Special Forces attacks over long distances can work (Entebbe, perhaps the best example) but they can also go wrong (US hostage rescue in Iran). They decided it wasn't worth the risk - especially once we were onshore