This video should provide some insight, but the gist of it is Argentina got
really careless with a military campaign they could have won, with many endemic issues in the junta and services that contributed to its defeat. Their basic assumption was that Britain would
not try to counter their invasion by force, and as a result, failed to plan for a possible counterattack. This led to a whole series of problems, such as planting ill-adapted northern conscripts in the cold islands as a garrison where better-acclimatized Patagonian troops could have been deployed (though, those would probably still be needed at the Chilean border at the time). Timing of the invasion was also ridiculous, failing to use the worsening climate and ongoing downsizing of the Royal Navy to their advantage by invading so early in the year, they've basically offered the British ample time and resources to mount a counteroffensive. Then, there's the interservice rivalry...
Yea, it's like a step by step guide on how to lose a very winnable war.