Firstly, the whole idea that the Falklands were empty is a lie, there was no permanent population, but the indigenous people did visit. Even if they did not, Britain abandoned the Islands in 1774, 9 years after they founded their settlement. They only decided to come back after Argentina started using the Islands in 1832, because while they did not want them, they did not like someone else having them either.

Secondly, the vast majority of the Global South does not recognise Britain's claim. I trust victims of Imperialism over an imperialist country when it comes to what constitutes as colonialism. AES countries support Argentina's claim, most notably Cuba, possibly the most anti-imperialist nation. They obviously do not want an outpost of British Imperialism in South America. Actual anti-imperialists like Che Guevara refuse to recognise British claims to the islands.

Finally, while I do not usually agree with Bad empanada, his video on the subject is a good takedown of all the arguments liberals use. The empty land myth has always been used to excuse colonialism from Ireland to Palestine. The idea a country can just claim ownership of land that no one is currently using, no matter where it is, uses childish logic to excuse horrific actions. The same people who refuse to express even a little doubt over Britain's claim would have supported the British Empire.

Most British "left wingers" start channeling Thatcher the minute the Falklands are mentioned (Stats for Lefties has always been a liberal, but I could not believe the lengths she went to to justify imperialism today). Corbyn is far from perfect, but at least he supported opening discussions with Argentina. The fact so many people on this sub, who are from an imperialist country, think they know better than those from the the Global South like Cuba is embarrassing. Why do you claim to be anti-imperialist, if the minute it comes to British colonialism you lapse? As a comparison, look at the comments on another international left wing sub linked above compared to the ones on this one.