first look at the map,

you see the UK anywhere near there?
and for the rest, well, there isnt an indigenous population at all (except sheep and even they where imported) there are some british living there but before the invasion it where only a very few.
i as an sort of anarchist offcourse also dont recognise the claims of argentine but from an statist perspective they make an hell of a lot more sense than the british.
The mind is its own place, and in itself Can make a Heaven of Hell, a Hell of Heaven. What matter where, if I be still the same, And what I should be, all but less than he Whom thunder hath made greater?
Here at least We shall be free