Overwhelming the people of Falklands (nearing 99%) voted to stay British. The people that have the right to self preservation. They want to remain in the hands of the British who will look after them, and offer them further referendums to determine their fate. The referendum is also Internationally recognised.
The Argentinians have a poorer economy compared to Britain, and controversially have human right violations. Why should someone impose that on the island residents?
The Falklands have voted democratically to stay within the British domain, so by that measure, the British are right to remain in the Falklands. The inhabitants are not hispanic people from Argentina, they're English speaking Brits. They have spoken, and they do not want to be taken over by Argentina.
Britain does not 'occupy' the Falkland Islands, rather the Falkland Islands are British. They are inhabited by British subjects who wish overwhelmingly to remain united with Britain. This was most recently expressed in a referendum. According to the international principle of self-determination, and a host of other principles, the Falklands are legally and rightfully British.
While the inhabitants of the Island voted to stay part of the Empire - they are all British in origin. The Island was captured to be part of an Empire. While I respect the will of the people you do have to consider the fact they are merely members of the Empire system itself...