Well, to be fair to the Argentine Administration, Nicholas Ridley had been pushing, with the support of the FCO, for a lease-back solution to the Falklands, similar to that in Hong Kong. This was moving slowly, but it seemed fairly clear that the FCO was working towards getting rid of the Islands. Add into that the Defence Review, the withdrawal of HMS Endurance, the Nationality Act (which affected the status of the Islanders), and it's not surprising that the assumption was made that Britain wouldn't fight to retain the Islands.
Also there was a perception (that they actually repeated to the incrudilous Americans who were attempting to secure a peace deal) that the British won't fight as they had no recent experiance of war having not fought any battles since 1945 - unlike the Argentine Military which had gained stacks of combat experiance as they had been recently fighting shotgun armed native american farmers....and students....and Nuns.
Also what probably did not help was the near weekly tabloid headline of some minister or another found on some common or heath 'hip deep' in a rent boy - giving the impression certainly to the Junta that the British government was a bunch of 'weak minded homosexual men' (no insult implied).
Now we here in this island were somewhat bored with the weekly news of such goings on in 1982, what went on in and around Whitehall 'stayed' in and around Whitehall, but to the Argentine Male of the Junta leadership Stock such things were not done by real leaders (again Im being somewhat generalist here) - and lastly - they told the US Peace envoy that Britain was led by a 'weak woman'.
At the last comment the Peace Envoys pretty much threw in the towel as they were unable and unwilling to follow the Junta leadership down the rabbit hole.
Its odd that had they simply waited then the Islands would have become Argentinian after a 100 years or so following some sort of leaseback deal with increasing ties to the mainland.
Now after so much blood and treasure (and dodgy football results) such a thing cannot now happen.
Certainly not within our life time.