The fact is the British foreign office had been trying to find ways to offload the islands on Argentina for ages. The British government felt they were an expensive nuisance that were an obstacle to better relations in the region. The Galtieri regime only invaded because they needed a boost in popularity. Negotiation is one thing, but military occupation quite another.
There is (or could have been) a legitimate discussion to be had about the history of control of the islands. Sure. But those who resort to pre-emptive military force, when facing no threat to themselves, have no business complaining when the resulting conflict goes against them. Suez is a good example of us learning that lesson the hard way.