As a Brazilian this "issue" is mind boggling to even have an argument over something. I have some Argentinian friends and I can only understand this in speaking with them, they grow up in Argentina with the Malvinas/Falkland being a question of pride, something that is unjust. But from a neutral standpoint it seems just so incredibly small to argue, much less fight over it. A cold, small, Alaska like little island. I wouldn't want it even for free.
South Americas is one of the only and fastest growing region in the World. Nearly all the countries are growing economically, Brazil is growing, Argentina is growing, come on, UK has its own issues to solve economically nowadays, Who gives a f*ck about this little island.
It's about the Principle.
Here's the Foreign Office's statement:
"The people of the Falkland Islands are British out of choice. They are free to determine their own future and there will be no negotiations with Argentina over sovereignty unless the islanders wish it."
There will be no talking with Argentina. The military ships are there to make sure if things escalate, the British citizens and interests are protected. Argentina is being a war-monger in this case.