I think this question is less historic-technical and more subjective. I guarantee that if you post to /r/changemyview you would get an answer from someone who solidly believes that the Falklands belong to Argentina and would most likely back up their argument with the facts you're looking for.
Sources, people. Write an in-depth comment yadda yadda... We've gone over this so many times now, a link to the rules is in the sidebar.
I've gone and removed this as your title is incredibly leading, and even with the edits in the body of your submission don't assuage concerns that you have already made up your mind, and merely want people to supply evidence that you are correct.
Now, that isn't to say there isn't a legitimate question here, but as you can see from the responses removed so far, asking it the way you did merely is a bat signal for partisan responses.
There are some very legitimate questions here, so if you do feel like resubmitting, feel free, but please consider phrasing it without giving the answer you already want in the title (ie. What can you tell me about the competing claims of the UK and Argentina over the Falkland Islands?).
Just a thing: Argentina has been a country since 1810 (first national government) or 1816 (Declaration of independence)
EDIT: Let me rephrase it Relative distance for the sake of relative distance wont be excepted as it is a lazy answer. The mere motion that positioning of land trumps the civilization that lives there is mere Colonialism something that Argentina claims is not there intent, there for it is exempt in this argument
I'm not comfortable with this. The mere positioning of lands has been reason to go to war over thousands of years, everywhere, civilization or not. Even worse you are making a case against colonialism and supporting the British point at the same time, which seems strange.
Anyway, you are missunderstanding the proximity issue. The argument comes from the islands being on the Patagonia continental shelf, defined geologically. Having Argentina signed the UN convention of law of the sea, it defines the argentinian claims on territorial waters and exclusive economic zones as dependant on the geological shelf.
And lastly, I don't feel you should come to /r/askhistorians with such a strong minded view. It comes of as pandering rather than curious.