Well, by request of man-bear-pig, and because I'm from Argentina, I want to share my opinion. Sorry for my grammar.
First, the Islas Malvinas (or Falkland Islands) are 480 km / 300 milles far off the Argentinian coast. The nearest point is Isla de los Estados, 340 km / 210 milles.
I think the story is something like this. Spain, with the different Viceroyalties, controlled South America. The Spanish controlled what is now Argentina, so they had the possession of the coast and travelled from the Atlantic Ocean to the Pacific Ocean. They discovered the Islands, but also did the British and the Dutch.
The visits from the English in the XVIII generated some problems with the Spanish. Then some French Count took possession of the islands in the name of the King of France, even founded a Port, but the Spanish protested, and finally the French admited Spanish soberany over the islands. They created the Governation of the Islas Malvinas.
The British founded a Port, but Spain achieved the retire of them in some kind of pact.
In 1810 a period of 6 years started in the Viceroyalty of Rio de la Plata, which ended with the Independence of Argentina. Between 1811 and 1820, the islands were abandoned by the Spanish. In 1820, the new government of Buenos Aires sended a ship to regain control of the territory. Luis Maria Vernet was conceded the explotation of the resources. He created some settlements in the island.
The actions of Vernet against some whaleboats made that the Lexington, a war corvette of the USA, attacked the Puerto Soledad instalations. The British arrived in 1833 with the HMS Clio, comanded by Captain Onslow, who told Vernet they were retaking possession of the islands in the name of the King of England. The Argentinian escaped to the continent.
Then happened what we all know in 1982. The dictators in Argentina weren't in their best times, so they tought that with the invasion of the islands they were going to obtain strength or something to continue. I think they just wanted to enter any war, because years ago we almost got into one with Chile, but never happened.
Thatcher also needed it, because England was in a crisis and with it, she "saved" the country.
I don't know if between 1833 and 1982 Argentina tried to do something with England, some kind of pact like the one of England and China for hong Kong. I think Peron, the president of Argentina in 1973, tried to do a pact of 50 years, but it's just a rumour.
I think the islands belong to us because they were of Spain, and Spain "gave them to us" with the independence, and because of the expedition of 1820. Also England is just waaaaay too far of the islands. Of course you can't just force generations of families to leave to England or make them Argentinians, I know that.
But don't worry, a war is not going to happen, we don't have the equipment and the soldiers to start a war. The one in 1982 was something stupid and we learned from that.
It's something that the government is doing to gain popularity, to make the people look into other direction while we are being murdered by thieves, while the vicepresident Boudou is being investigated for corruption, while the country is being sold to foreign companies so they can extract gold, while they are doing their negotiations, while people still disappears and while the President Cristina Kirchner is in the middle of a argument with the Mayor of Buenos Aires, Mauricio Macri.
In my honest opinion, I don't want the islands right now, because it is all a play of the goverment, I dislike this goverment and I hate Cristina.
Even if we get the islands, what are we going to do with them? Probably sell the resources and the lands to friends of the politics, so I don't want that to happen.