The myth of Che Guevara is seductive and lush. It's the story of an Argentinian rich-boy who was so shocked by poverty he became a Robin Hood fighting alongside the poor, until eventually he was murdered by the CIA. But the reality of Che Guevara is very different. The facts show that he was a totalitarian with a messiah streak, who openly wanted to impose Maoist tyranny on the world. He was so fanatical that at the hottest moment in the Cold War, he even begged the Soviet Union to nuke New York or Washington or Los Angeles and bring about the end of the world.

It is true that Che's story begins with a motorcycle journey across South America. The young man was repulsed by the gap between the swanky transplanted European culture in which he lived and the starving misery of the indigenous peoples. He could see that this was caused largely by America's habit of smashing local governments and replacing them with dictators prepared to slobber over US corporations. But he concluded from that journey – gradually, over a few short years – that there was only one solution: the imposition of authoritarian communism, by force, everywhere. He chose not to see that this system, wherever it is tried, makes people even poorer still, invariably spreading famine, starvation, and terror.

Since the Soviet Union was too soft for his tastes, there were only two countries that Che found truly admirable: Maoist China and Kim Il Sung's North Korea. He bragged that there was "not a single discrepancy" between Mao's world view and his own. As Che was happily fawning over Mao in the flesh in Beijing, in the surrounding countryside there was an epidemic of mothers cutting off the flesh from their inner thighs to feed it to their starving children. The programme that caused this biting hunger – the mass collectivisation of the farms – represented "true socialist morality", Che said. The dictator killed 70 million people in the end, cheered on by his guerrilla friend at every stage.

Of course, Che's defenders act as if this was the only choice confronted by Latin Americans: you were either for US-imposed market fundamentalism, or for Maoist Communism. But you don't have to look very far in Che's life to see that this is a lie. His diaries show that he was constantly appalled to discover that almost everyone around him, including the revolutionaries fighting by his side, did not share his Maoist vision for the future. His first wife, Hilda Gadea, was a social democrat. She wanted to depose the US-backed tyrants – and then replace them with moderate, Swedish-style mixed economies. Che ridiculed and pilloried her as "bourgeois", before abandoning both her and their child. The ordinary Cubans he fought alongside on the Sierra Maestre also wanted to create a democracy with a mixed economy. Disgusted, Che noted in his diary: "I discovered the evident anti-communist inclinations of most of them."

When Che and Fidel Castro's guerrilla army seized power in Cuba, he was immediately – and to his delight – put in charge of the firing squads. He instituted a system of 'trials' that lasted just a few hours, with himself as sole judge. They invariably ended with the low-level functionaries of the Batista regime being lined up and shot. Che's public declarations from that time are blunt. "All right, it is dictatorship," he shouted at one point. "It's criminal to think of the needs of the individual." He even banned Santa Claus, saying he was an "American imperialist import."

The friend who had travelled with Che on the famous motorcycle journeys, David Mitrani, was shocked when they met up in Havana after the revolution. He could not understand how Che's compassionate response to poverty all those years ago had led him to announce he now wanted to become an " effective, violent, selective, and cold killing machine".

Che's fanaticism reached its peak in October 1963, when he seriously advocated a course of action that would immediately end life on earth. Che had implored the Soviet Union to place nuclear missiles on Cuba. He knew the US would interpret this as an act of aggression and probably retaliate with nuclear weapons – but he said that "the people [of Cuba] you see today tell you that even if they should disappear from the face if the earth because an atomic war is unleashed in their names... they will feel completely happy and fulfilled" knowing the revolution had inspired people for a while. Che did not say how he knew the Cuban people would be delighted to die of radiation sickness, their hair burning on their heads and their skin slopping from their faces.

The Soviet Union followed Che's advice – and the world came closer to nuclear annihilation than at any point before or since. On the American side, maniacs like General Curtis LeMay implored Jack Kennedy to nuke Moscow immediately. On the Soviet side, Che Guevara played exactly the same role. He urged Khrushchev to launch a nuclear strike, now, against US cities. For the rest of his life, he declared that if his finger had been on the button, he would have pushed it. When Khrushchev backed down and literally saved the world, Che was furious at the "betrayal". If Che's recommendations had been followed, you would not be reading this newspaper now.

None of these facts are seriously disputed by historians; they are simply skidded over by Che's defenders, who stick to romantic generalities about how he stood for "honesty" and "revolution". But Che Guevara is not a free-floating icon of rebellion. He was an actual person who supported an actual system of tyranny, one that murdered millions more actual people.

If the small lingering band of communo-nostalgists who still revere Che were honest about continuing his life's work, they would have to form a group called "Left-Wingers for Creating a Universal North Korea, Prior to Universal Death in a Nuclear Winter." I don't think they would find many recruits.