Well actually they hoped the British wouldn't fight over them. Argentina successfully occupied Southern Thule without British repercussions. The Navy then ordered the HMS Endurance back from the Southern Atlantic (the last vessel they had there) and the Parliament issued a law stating that the inhabitants of the Falkland islands are no citizens of the United Kingdom.

Furthermore Argentina had a huge strategic advantage. The Falkland islands were directly in front of their doorstep. They had the 'inner lines' despite being the aggressive force.

Also the British Navy was not prepared for a war that far from home. They were specialised on fighting the sowjet navy in the GIUK gap in the northern Atlantic should the cold war get hot. They discontinued service on nearly all of the Carriers and had little Anti Aircraft capabilities. Their main focus was fighting submarines (of which the Navy of Argentina had 4, two of those modern German builds, two German builds from the Second World War.

The armed forces of Argentina were not that bad themselves. They had a couple of modern aircrafts (French made), roughly 180.000 men at arms and their Navy was equipped with Exocet missiles. They knew the USA were not gonna help the UK (the USA were very anti-imperalistic) so overall it seemed prudent to believe that the UK would not take the risk of fighting a war thousands of miles away for a hand full of islands nobody needed.

Hi, you may be interested in a few earlier discussions

• Why did the Falklands war happen? - a nice long Q&A-style thread featuring /u/k1990. About 1/4 down the thread, /u/Borafan asks your question

• Did the Argentinians think they could win the Falklands War against the British, or was it more to prove a point, albeit while starting armed conflict? - featuring /u/an_actual_lawyer and /u/tc1991

• Did the Argentinian Military think it was possible that the British could retake the Falklands and what did other powers think of the military chances of a successful British operation to retake the islands

• How "out of the blue" was the Argentine invasion of the Falklands?

I recall reading an story that when the British Army was preparing the invasion to the falkland island, the BBC leaked the whole operation. This somehow made the argentinians believe that if the british really had the intention of invading the falklands they will not reveal their whole plan on TV, is this even true?