In 1960, a 28-year-old writer named John Updike published his second novel, Rabbit, Run. The New York Times called it a “shabby domestic tragedy,” but also “a notable triumph of intelligence and compassion”. It singled out his stylistic achievement in particular, praising him for having created a “perfectly pitched voice for the subject”. This early review set the tone for what would follow, and for many years Updike, Philip Roth and Saul Bellow were hailed as a kind of unquestioned trinity of the best modern American novelists. When he died in 2009, 23 novels, countless stories, essays, and a few volumes of poetry later, the New Yorker pronounced him “one of the greatest of all modern writers, the first American writer since Henry James to get himself fully expressed, the man who broke the curse of incompleteness that had haunted American writing.” Even bearing in mind that the New Yorker had been, in essence, Updike’s house magazine for 50 years, this remains praise of an order few writers will ever achieve. Whether it’s true is, of course, another question. It was Rabbit, Run that started it all, and now Radio 4 has decided to run Rabbit as its Book at Bedtime, giving listeners a chance to judge for themselves.

Eventually Updike would write four novels about Harry “Rabbit” Angstrom, his suburban everyman. Angstrom is too intellectually limited to be considered Updike’s alter ego; call him instead Updike’s altered ego, an artfully reconstituted, carefully delimited, sometimes monstrous, sometimes pathetic, persona by means of which Updike surveyed US postwar life. The New York Times described Angstrom, a former basketball star feeling trapped by his suburban life of marriage and fatherhood, as “an older and less articulate Holden Caulfield”; it’s not a bad comparison. Updike helped map what later became known as “Cheever country”: the white, affluent, suburban landscape of stunted hopes and spiritual anomie through which Harry Angstrom will take his picaresque journey. Updike’s bitter joke, however, is that Rabbit can’t run.

In this sense, Rabbit, Run is a clever subversion of an old US motif: the man on the run from the suffocating effects of society, as if a tragicomic western had lost its way and ended up trapped in southeastern Pennsylvania. But this tradition is also endlessly troped as men escaping the domestic snares of women, a tradition which Rabbit, Run cheerily joins. From Huck Finn lighting west for the Territory to escape Aunt Polly’s efforts to “sivilize” him, to Charles Ingalls, with his itch for travel and his wife who insists they build a little house on the prairie for their girls, to Sal Paradise and Dean Moriarty taking off on the road: US popular culture is riddled with stories of men who yearn to be free, and the women who yearn only for them not to be. These are doubtless very enjoyable stories for men to read, but for women they can be quite irksome. Always cast as the smothering presence, the old ball-and-chain pinning men down who would otherwise roam wild, women end up symbolising dependence and paralysis while men get to symbolise independence and liberty. I know which one I prefer.

At the beginning of the novel, 26-year-old Harry climbs into his car and leaves his depressed, pregnant young wife, Janice, and heads south with dreams of Floridian paradise. He stops for fuel and directions; instead of being given a map, he is given advice that sums up the novel: “The only way to get somewhere, you know, is to figure out where you’re going before you go there.” Drift is not an option; Harry, who shares a rabbit’s proclivities for procreation, also shares its legendary inability to win the race after starting out in front. The imperative of the title means that some unseen voice is telling Rabbit to run, perhaps suggesting his internal compulsions, or some kind of higher power – whether of the authorial or spiritual kind – urging him on. But by 1960, there was nowhere to run: the frontier was well and truly closed, and all that was left for men was the mock heroism of suburban tragicomedy, running in circles.

Part of the problem for women reading Rabbit, Run is that Updike made the decision to have Harry choose between two stereotypes: after returning home Harry leaves Janice again, this time moving in with a prostitute. Janice, the asexual mother, is small, childish, bony; the prostitute Ruth is voluptuous, large, welcoming and fecund. There are those who argue that Updike is ironising this stereotypical choice, showing how narrow and foolish it is, and it is true he gives both Ruth and Janice slightly more complex interior lives at points in the novel. But Updike doesn’t imagine them really having any desires that are not centred around domesticity or keeping a man, whether because, as in Ruth’s case, they fall madly in love with him or, as in Janice’s case, they merely want to avoid social humiliation. Either way, to judge it against a modern metric, it’s fair to say Rabbit, Run fails the Bechdel test (requiring that two or more female characters discuss a topic other than men).

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In 1960, Richard Gilman described Rabbit, Run as both a “grotesque allegory of American life, with its myth of happiness and success”, and a “minor epic of the spirit thirsting for room to discover and be itself”. It remains the case that only male characters get to be treated as allegories of US life, grotesque or otherwise. Mankind can denote all humanity; womankind can only denote all women. Surely part of “the curse of incompleteness that had haunted American writing” was its inability to recognise the full humanity of half of humanity – the female half; and if Updike is to be put in the same class as Henry James, then he should be measured by the same standards.

When Henry James looked at women, he imagined that they thought like him. When Updike looked at women, he imagined that they thought about him. For me, questions about misogyny in literature are of limited efficacy at best; I prefer judging a novel by how well it thinks about the problem it has set itself. Rabbit, Run is a novel ruminating on the costs of patriarchal society that is partly limited by the very limits it depicts, but cannot quite overcome. The incompleteness remains, while the novel endures.

• Sarah Churchwell is professorial fellow in American literature at the University of London. Rabbit, Run is Radio 4’s Book at Bedtime until 28 April.