I was one of the guilty men of 1982. The previous year, in conversations at my college in Oxford, where my colleagues and I dismissed the Falklands dispute as trivial, visiting Argentinian top brass got the impression that Britain would not fight for so pointless a prize. Indeed, few British people cared about "a far-off country" of which they knew little. The inference, however, that they would not fight over a matter of principle was false.

Britain had virtually nothing of any material value at stake in the islands at the time of the invasion on 2 April 1982. But to allow the Junta to invade the Falklands with impunity was almost as unthinkable as allowing Hitler to seize Poland. Recourse to violence imperilled the peace of the world, because the differences between the sides could have been sorted out with modest compromises. Today, 30 years after the war, two developments have put the continuing controversy beyond hope of a reasonable outcome: first, the effects of the war; then a revolution in the islands' economic prospects.

The war exacerbated feelings and made a negotiated outcome hard to imagine. Both sides worked themselves up into silly self-righteousness and unreasonable mutual condemnation. On the day the invasion started, an Argentinian friend of mine got into a taxi in Park Lane without knowing that hostilities had broken out. "I am from Argentina," she announced cheerfully in reply to the cabbie's idle question about her provenance. "Out of the cab!" he ordered. "I'm not having no bleedin' Argies."

A few months later, when the war was over, my wife was surprised by a rather more courteous gesture from an Argentinian pilgrim on the steps of the cathedral of Compostela. He solemnly shook her hand, explaining that he exempted her from responsibility for the malevolence, piracy, war crimes, atrocities and evil aggression committed by her government. The pilgrim was nicer than the cabbie – but both showed the insuperable ignorance that divided the sides.

In some ways, the war did both countries good. The British enjoyed a rare opportunity for self-congratulation on a victory whose heroics they exaggerated and whose brutalities they largely overlooked. Argentinians, meanwhile, could replace dictatorship with democracy and console themselves with thought that Albion had only triumphed, as usual, by perfidy – shooting the Belgrano in the back and reimposing colonialism at bayonet-point.

Partly in consequence of these comforting delusions, neither side could recall the war with realism, or assess its folly with objectivity. To understand Argentina, one must appreciate that the average citizen conceives his country's past as a history of failure and frustration. God, Argentinians think, made theirs to be a great land, but at every opportunity they have wrecked His handiwork, allowing dictators to repress their virtues and foreigners to steal their resources.

The conscripts' inertia in the face of British forces was understandable – indeed, sensible, as it would have compounded folly to give one's life for valueless islands or gratify the revolting vanity of General Galtieri and his cronies. But so abject a defeat was a source of shame and a cause for evasion in a country whose national anthem ends with the cry, "Let us swear to die with glory!"

The British, in turn, were victims of the gypsy's curse: "May you have wars – and win them!" Victory involved terrible costs for a penurious economy and imposed further waste of resources on defence and investment. Somehow, the costs had to be justified and, if possible, recouped – making a future settlement with Argentina harder than ever. The opportunity to offload a futile, valueless colony had turned into an obligation to hold on to it at any price. Then economic changes began to set in, problematising ever more hopelessly the prospects for lasting peace. First, in the 1990s, the offshore fisheries became highly productive, and fleets from all over the world wanted licences. Then – decisively – in the following decade, the chances of profitable oil exploitation multiplied.

Once rumours of oil seep out, they poison negotiations as surely as slicks blacken the sea. The parties in the dispute go on uttering unconvincing rhetoric. Monotonous cant about the islanders' rights of self-determination dominates language on the British side, as if the handful of people concerned could not be easily satisfied – indeed, bought off – with so many resources to hand. Argentina continues to belly-ache about the injustice of Britain's original seizure of the islands in 1833, as if any of that mattered now. Continued British rule rests on the bottom line. When the islands were unimportant, their fate would have been easy to settle. The magnitude of the problem has grown with the magnitude of the stakes.

There was a moment in the past decade when Britain and Argentina might have agreed to share the bonanza. But, just as the Junta blew the chance of a rational solution by an act of folly in 1982, so President Nestor Kirchner wrecked hope of a settlement in 2007 by repudiating unilaterally existing resource-sharing protocols. He thought he was commemorating the 25th anniversary of the war, distracting his electorate, striking a heroic pose, and making a calculated effort for a better deal.

He was wrong on all counts. He counted Argentina out of a stake in the mounting promise of profits and made it impossible for British governments to give back what he had forfeited. His widow, who now occupies the presidency, has been left with no option but to try to justify or conceal his error retrospectively. Her bluster cannot change the situation. It can, perhaps, obscure the truth. In either event, the problem remains insoluble: Argentina cannot renounce her claims. Britain cannot accommodate them.

Today the islands are grossly under-defended and, if Argentina were to invade, there would probably be little international support for Britain this time round. Big oil would shift allegiance to the victors. It won't happen – but only because Argentina is now indelibly democratic and her citizens will no more vote for war than hens will for Easter. Instead, we can look to a long stalemate, while the islanders get rich and relations between Britain and Argentina stagnate.

When the next opportunity for a settlement comes – probably sometime in the next 20 years, with renegotiation of international agreements on Antarctic exploitation – it may be possible to transfer sovereignty quietly, while divvying up amicably such resources as then remain. Maybe then we shall be able to admit the truth: it doesn't matter who rules the Falklands – or whether we call them the Malvinas.

Felipe Fernandez-Armesto's books include 'The Americas: A History of Two Continents'