Argentinians want the island, but the people who actually live on the island want to stay in the UK, and Argentinians don't have much appetite for military action

https://theconversation.com/the-falklands-war-40-years-on-why-las-malvinas-are-still-such-an-emotive-issue-in-argentina-181364

https://yougov.co.uk/topics/politics/articles-reports/2012/04/10/falklands-war-britain-and-argentina

The Falklands War, 40 years on: why 'Las Malvinas' are still such an emotive issue in Argentina

Four decades after it’s invasion was defeated by a UK ‘task force’, Argentina remains committed to ‘recovering’ the Falkland Islands.