OK - lets look at the question of who should own the Falklands....
A British chap by the name of John Strong sailed to them in 1690. At the time - the region was unpopulated. The French were the first to settle the area, in 1764 - resulting in de facto control. So initially we have a claim between the French and British.... In 1765 the British landed and claimed the region. They later found the French Colony and the first disagreement about who had claim began. However, the French basically sold their control to the Spanish in 1766 and vacated the area. So now it becomes a British claim and a Spanish claim - though the Spanish claim is now "second-hand". Then, in 1770, the Spanish expelled the British colony via "expedition" - a nice way of saying they got run off by an armed force. In 1771, over the threat of war, the Spanish backed off and the English returned to the region. However, due to the economic strains of the American War of Independance, the English left the Falklands in 1776. They left a plaque claiming the land as British at the time, but also left total defacto control to the Spanish. The Spanish then left the Falklands for good in 1811 - also leaving behind their own plaque claiming the land as Spanish. Note that during this time - one country claiming the Falklands is not mentioned..... that would be Argentina. Why would that be? Because Argentina didn't even EXIST at the time. It is interesting to note that British (and American) seal hunting ships continued to put in to the region though it now was unpopulated again. Now - in 1816 the people of what is now Argentina declared independance from Spain, and in 1820 actually realized that through conflict. They became known as the "United Provinces".
We now move forward to 1826 - and enter Luis Vernet - a German by birth. He requested the authority to colonize the islands. Who did he ask? Not the "United Provinces" - but he DID ask the British. When that attempt failed - he again asked the British in 1828 for the chance to try again. The reason this is important is because Argentina's claim rests heavily with Vernet, as we will soon see. Vernet was a merchant, and the United Provinces owed him quite substantially, so when he succeeded in seeing the area settled in 1828, they made a deal with him. They would appoint him "governor", basically giving him the region as payment. In 1828, the Argentine government granted Vernet all of East Falkland, including all its resources, with exemption from taxation if a colony could be established within three years. He took settlers, including British Captain Matthew Brisbane, and before leaving once again sought permission first from the British Consulate in Buenos Aires. The British asked for a report on the islands for the British government, and Vernet asked for British protection should they return.
[So, in 1829, Vernet was named Governor by the United Provinces, though its quite important to note that he continued to send "reports" back to the British Consul (which shows he continued to accept and recognize the British claim to the Falklands). In 1831 Vernet seized the American sealing ship Harriet (he had also siezed two other ships) and the US sent the sloop Lexington to the region with orders to recover the Harriet. This the American warship did, while taking Vernet into custody. The colony was evacuated - the Lexington giving the choice to the colonists to stay or leave, and offering them transport to Montevideo. The majority chose to leave, except for a few "cowboys"who remained in the interior of the islands (and not within the settlement inself). Vernet then sold most of his holdings in the Falklands to a British merchant and never returned to the Falklands.
The United Provinces - aka Argentina - tried to turn the region into a penal colony - with no success. The new leader was murdered and no control was ever established. In fact, the only "civilized" part of the area is Port Louis - and it is manned by BRITISH mercenaries who keep the riff-raff that the UP had sent over (trying to create the penal colony) at bay.
Meanwhile, events play out with Vernet and Britain makes the decision that its sovereignty over the Falklands should be asserted - else those uppity Americans might just decide to take a liking to the area. In 1833 the HMS Cleo arrives in Port Louis and the Captain makes note the settlement is flying the wrong flag - since it happened that it wasn't a British flag. He also sent the Argentinian bureacracy packing, and they left without firing a shot. Thus the first permanent settlement of the Falklands was established in 1833 - by the British. Vernet's deputy was allowed to return to the Falklands and his position under the condition that he did not traffic - as Vernet had done - with Argentina.
Its also quite interesting to note that Argentina offered to relinquish any claim to the region - in 1841 - for the cancellation of debts. Britain refused to consider the offer.
Britain has repeatedly offered (in 1947, 1948 and 1955) to let the matter be mediated by the ICoJ at the Hague - Argentina has refused all three offers.
Argentina's claim to the Islands stands on its investure with Venet - claiming his acceptance of title from them showed the leader of the colony recognizing their claim to the region. It also arises from the Nootka Sound Conventions - a treaty between Spain and Britain dating from 1789 that states that the coast of South America and its islands were Spanish Territory. However - the Spanish unilaterally repudiated those conventions in 1795, making the agreement null and void.
Thus it boils down to this....
Britain found it. France settled it. Spain then had a second-hand claim to it. Argentina then tried to claim it after becoming independant - meaning that the the Argentinian claim is now "third hand". If one were to consider their claim valid - they gave the region to a merchant in 1829 - who ultimately ended up selling the majority of it to a British citizen! As for the Nootka Bay agreement - the idea that Argentina could think a country would respect a contract with a THIRD party and the agreement was already terminated (and not by the British) is ludicrous. History shows that Argentina has tried to use the Falklands as payment for its debts - and not just once. First they used the Falklands to pay Venet - then they tried to pay of London debts with the region in 1841 - and now the Argentinian government sees economic profit once again in the Islands - and so it again tries to lay claim to them.
Finally - and to those Argentinian members of subsim - this does NOT reflect on you, but rather your government - but there were no indigenous people in the region - and the people that are there now want to remain under the British flag. Given the bloody history or Argentina (which not all of that is the fault of Argentina - and what country doesn't have blood on its hands) - its time to respect the rights of those that live there - especially since Argentina gave the Falklands to Venet and he sold them.