It was in a middle of a major economic crisis. They had just retired their last traditional aircraft carrier, the Ark Royal, and had to rely on two light carriers equipped only with what was considered back then a funny and unreliable contraption/scientific project, the Harrier jets. For bombers, they had the Vulcans, planes designed back in the late 1940s.
They also had to build a supply line that was 12,000 KM long, which they new they could not sustain for long periods of time. The British task force had with it just enough ammo, supplies and flue to last but a few weeks off the Falkland's coast. They had to either land or retreat.
Argentina, on the other hand, had at the time the most advanced military of any non-aligned nation. The Skyhawks, Mirages and Daggers had just been proven in great combat planes less than 10 years before, during the Yom-Kippur conflict. The navy operated one of the most advanced combat system in the world, the combination Super Etendard/Exocet, that had just entered in operation in France 2 years before the Falkland conflict. It was something so incredibly advanced at the time, that even the British had nothing comparable on their arsenal back then. Argentina also had very modern german submarines and torpedoes, and had the Argentines used them correctly, they could have sunk the entire British task force. All of that operating just a few hundred kilometers from the Argentine coast.
The iron lady took a tremendous political risk by trying to retake the island by force, as it was as far from a "sure thing" as one could get.
