We all know mum and dad can really inflict damage on a child's psyche, even though they may have only the best of intentions. Matt Ross' Captain Fantastic is a film about a father whose love for his children might be ruining them for life, even as he prepares them to meet every conceivable challenge.

In what must rank as one his best-ever performances, Viggo Mortensen is superhero, Ben Cross, a former academic raising six kids in the woods of north-western America.

The movie begins with a startling rite of passage as the oldest son, Bodevan (George McKay), stalks and kills a deer with a hunting knife. Soon the bloodied hunter is surrounded by a tribe of savages, their faces covered in mud. Is it family or a cult? Such ambiguities are not easily resolved in a story in which it becomes increasingly hard to decide whether Ben is equipping his children with superior skills or turning them into freaks with no point of contact with the world.

Ben is both a visionary and an authoritarian leader who has brought his children to an exceptional level of physical and intellectual accomplishment, but his quest for perfection is also a form of mind control. Each of the kids has a unique name invented by their parents, making them sound like characters from a Tolkien story: Bodevan, Kielyr, Vespyr, Rellian, Zaja, Nai.

In the Cross household, Christmas is ignored but Noam Chomsky's birthday is celebrated. From an early age, the children engage in daily calisthenics and advanced rock-climbing. They learn self-defence, and how to use a knife and a bow. Ben's children can discuss Marxist dialectics, Jared Diamond, particle science or Dostoyevsky, but have no knowledge of the popular culture that dominates the minds of their generation. They are Übermenschen in the making, and this is slightly disturbing.

Idyll broken

Ben's wife, Leslie, has been away undergoing treatment for bipolar disorder and, when word comes through that she has killed herself, the idyll in the woods takes on a different complexion. The family decides on a rescue mission to save Leslie from the full church service and burial being organised by her wealthy father, Jack (Frank Langella).

This means a pilgrimage to New Mexico on a ramshackle bus – as the scenario switches from Swiss Family Robinson to Little Miss Sunshine. During the journey, they will steal food from a supermarket in a guerilla operation and endure an awkward visit with relatives. At a caravan park, Bodevan will meet a teenage girl and realise the depths of his unworldliness.

Because Jack blames Ben for his daughter's illness, and ultimately her death, he has no sympathy for bold experiments in home-schooling. Jack is a former army man who believes in all the bourgeois, nationalistic virtues that Ben derides. When the family and grandparents have overcome their initial tensions, Jack pressures Ben to leave the children with him and Leslie's mother, Abigail (Ann Dowd). It's easy to refuse, but circumstances gradually force Ben to reconsider.

This is where the story gets complicated as Ben has to ask himself – probably for the first time – whether his pedagogical methods may be doing more harm than good. He hasn't abandoned his conviction that the world is a hopelessly corrupt place, but withdrawal to the wilderness may not be the solution.

If Ben had been an extreme right-wing survivalist bringing up his kids on a diet of conspiracy theories and racist ideology, the movie would be a horror show and we'd be desperate to see the children removed from their tormentor. By making him a dedicated humanist, Matt Ross has created a fund of sympathy for the character.

Utopian fantasy

Ben may be arrogant, dictatorial and abrasive, but he wins arguments with logic, not with violence. The way he is raising his children taps into a deep vein of utopian fantasy that probably begins with Jean-Jacques Rousseau's musings about the state of nature, and finds a more focused exposition in Emerson's Self-Reliance (1841) and Thoreau's Walden (1854). America in the late 19th century would see the greatest upsurge of popular utopian thinking until the advent of the counter-culture of the 1960s.

Ben is an American Romantic, a dreamer who has dared to turn his principles into actions, but in many ways he remains an academic theorist more concerned with winning an argument than considering the wider consequences of his beliefs.

We can admire his idealism but feel disturbed by the sense that he is using his family as part of a bold experiment. He is no soft liberal who feels that kids need to be kids. The children in the Cross family are treated like adults and expected to behave as such, even if there is love and fun amid the discipline. The problem is that human personalities are too various and unruly to be moulded by a program. Ben may be a benevolent dictator but he shares in the common desire of all despots to remake the world in his own image. It's a fantasy that neither politics nor parenthood has yet been able to achieve.