Riggan Thomson – once the star of the Birdman films, now a big-name Broadway newbie – leaves his dressing room at the St James theatre in New York and winds through its labyrinth of backstage corridors. The paint is peeling, the pipes are bare and the wallpaper would better suit a 1970s B&B. He passes all sorts en route – silent, oddball technicians; a prompt asleep in his chair – before waltzing into the wings, stepping on to the stage and sliding, seamlessly, into a scene and into character.

Film critics have, inevitably, read Birdman as a film about film: a comment on the vanity and vapidity of blockbuster Hollywood, on superstars and superheroes and “art” driven purely by box office rankings. That’s all in there, for sure, but Alejandro González Iñárritu’s film is far better on the subject of the theatre. It might stake a decent claim to be the best film about theatre ever made.

Alejandro González Iñárritu directs Edward Norton and Michael Keaton in Birdman at the St James theatre, New York. Photograph: Allstar/Fox Searchlight Pictures

Because Birdman gets so much right. It nails that slippage between on- and off-stage, between fiction and reality; the way a play can bleed into an actor’s life and big curtain-call smiles mask seething resentments. It gets all the unvarnished scuzz of backstage life behind Broadway’s glitzy frontage, and the crackle of sexual chemistry between co-stars. It picks at the battle between ego and insecurity, brilliance that needs constant reaffirmation, and appreciates the catatonic terror of stepping out in front of an audience.

Theatre – and I write this with admiration and awe – is full of freaks and weirdos. Brilliant freaks and weirdos, yes, but freaks and weirdos nonetheless. Birdman totally gets that. Its theatre is a safe house of sorts. Antonio Sanchez’s drums, the symbol of improvisation and liveness, flare up whenever Riggan steps out into the bustle of New York, only simmering down when he’s safely back inside. It’s a place of fixity and certainty, of routines repeated night after night.

As such, it suits damaged, brittle people, those unfit for real life. People like Riggan’s daughter Sam and his co-star Mike Shiner. When the two of them play “truth or dare?” on the theatre roof, Shiner only ever picks truth. His honesty looks valiant, but it hides its opposite: he daren’t dare. The actor won’t act, can’t act – not in the real world, not in any meaningful way.

Edward Norton and Emma Stone on the St James theatre roof in Birdman.

Theatre shelters these people. It keeps the real world at bay, and that’s what makes it such an anachronistic artform. Riggan, as Sam points out, has adapted a 60-year-old book for a roomful of rich, white, old folk. A YouTube video of him weaving through Times Square half-naked gets 350,000 views in an hour. Birdman itself reached millions worldwide. In comparison, theatre doesn’t matter.

And yet, on the inside, it matters intensely. It’s everything. It aims at truth. Shiner claims to “pretend just about every place else, but not out there” – not on stage. Theatre, as Birdman sees it, manages to hold the complexities and contradictions of the world. But only in a flickering, unstable moment. That’s Birdman’s real bullseye: it’s about presence and liveness. That’s why its camera never seems to cut. It’s why, whenever actors take flight and forget about their audience, whenever life catches people off guard, when fights kick off or drink kicks in, Iñárittu bathes his cast in light and colour. Yet those moments, like the theatricals themselves, are fragile.

And that’s where Birdman makes theatre a metaphor for life – and earns its bloated subtitle: or, The Virtue of Ignorance. To live truthfully, in the moment, means forgetting about your audience. In life, unlike in theatre or film, they simply don’t exist.