Self-determination does not apply here because the current population is not indigenous but was implanted after the UK forcibly took the islands in 1833, displacing the original Argentine population. The UN considers this a decolonization issue, not a matter of self-determination.
The argument that the islanders “chose” to remain under UK control ignores that democracy cannot legitimize colonial occupation. A referendum by settlers cannot override international law, just as a vote by European colonists in Africa in the 19th century wouldn’t justify occupation. The UK has consistently refused to negotiate, violating UN resolutions and international norms.
> Argentina claims that the population of the islands was expelled in 1833;[11] however, both British and Argentine sources from the time, including the log of the ARA Sarandí, suggest that the colonists were encouraged to remain under Vernet's deputy, Matthew Brisbane.
So again, I repeat: this is all very well documented by this point. The other commenter also already pointed out the other issue in your text here so I'll leave it at this.
The argument that the islanders “chose” to remain under UK control ignores that democracy cannot legitimize colonial occupation. A referendum by settlers cannot override international law, just as a vote by European colonists in Africa in the 19th century wouldn’t justify occupation. The UK has consistently refused to negotiate, violating UN resolutions and international norms.