Maybe because Britain (Well the English) were the first people to actually sight the islands. Claimed the islands since that day and has never renounced the claim ever. Even when the Spanish and the French had settlements so did the British. Both Spain and France renounced their claims BEFORE Argentina was a country. Again Britain never did.
It would be like 3 people co owning a car. 2 of them no longer legally or morally claiming any kind of ownership over it. But the son of one of the 2 keep on crying about it because it was they believed that their dad gave them the car even after the dad renounced ownership.