My understanding is that no one even wanted the islands until they found oil nearby.

Bingo!

there’s no reason to argue for Argentinian ownership of the Falklands. Hell, Argentina taking ownership of the Falklands is more colonialist than UK maintaining ownership

The United Nations says otherwise.

The Wiki page is really interesting reading on the ownership of that island, really jumps around over the centuries.

This one part of the article really jumps out at me…

That self-determination is further rendered inapplicable due to the disruption of the territorial integrity of Argentina that began with a forceful removal of its authorities in the islands in 1833, thus there is a failure to comply with an explicit requirement of UN Resolution 1514 (XV).[93][94]