I love discussing this topic with Argies, it's likely the only way to discern who's semi-rational and who's a Nationalist idiot.
Here's my take:
On the War: On the verge of his gang's collapse, a drunk dictator was not able to organize another massive sport event to distract the populace from the random killings so they invaded a disputed territory, and here's the saddest part, granted its inhabitants rights a "Continental" Argentine could only dream of at that time (like the right not to be randomly shot). The schizophrenic masses loved it! --- at the expense of provincial cannon fodder, proving Nationalists value their National symbols more than their National Citizens. Maggie T not only had the right to defend the Kelpers but the duty.
On Sovereignty: There are almost no places in this Earth that had no native population by the eve of the Renaissance. The Falklands was one of those places. Its population came to be from British subjects from across the world. When Spanish America gained independence (thanks to the British) the southernmost frontier was Fuerte Bulnes, in Chile, and it was just a loosely defended military outpost. The actual frontier of the "Capitania de Chile" was around Araucania (north of Pt Montt), and the Southern frontier of the Virreynato del Rio de la Plata, later the United Provinces, was farther North, around Lujan. Practically all of Patagonia was uncharted, uncolonized and up for grabs.
Basically Argentina, as heir of the Virreynato, has more right to all of Paraguay and Chile, and parts of Bolivia, than to its own Patagonia, even less to its pre-colonized outlying islands.
How much sense would it make if a fascist leader took over Canada and decided to unite the country to "re-conquer" Saint Pierre et Miquelon? How much sense would it make for Demoratic Canada to claim those French Islands?