It's not clear whether the Coen brothers have read the works of Blake Snyder, but anyone who has done will appreciate Inside Llewyn Davis in a rarefied way, particularly its feline symbolism. Snyder, for the uninitiated, is best known for Save the Cat!, a screenwriting guide that, depending on your point of view, either lays bare the mechanics of movie storytelling, or reduces them to an idiot-proof template. The book, published in 2005 (Snyder died in 2009), has become almost a cheat sheet for screenwriters, instructing you what to put where on a minute-by-minute basis. You start with a strong opening image, state the story's theme by page five, break into Act 2 on page 25, and so on. The fact that Snyder's greatest success as a screenwriter was Stop Or My Mom Will Shoot! has in no way undermined his authority.

One essential ingredient of Snyder's formula is, predictably, the "save the cat" moment. "It's the scene where we meet the hero and the hero does something – like saving a cat – that defines who he is and makes us, the audience, like him," he writes. It's also been called the "pet the dog" trope), you'll follow a movie character anywhere, even if they go on to steal, cheat, kill, or commit any atrocity short of harming an animal (if you see a character kicking a cat, chances are they won't make it to the end credits). Call it a trick of the trade – one of the most common reasons for a script rewrite is to "make the character more sympathetic", and the insertion of a save-the-cat scene is a quick fix. It's by no means a new phenomenon. In his book Making Movies, Sydney Lumet recalls screenwriter Paddy Chayefsky moaning in the 1970s how "the studio always wants a 'pet the dog' scene so they can tell who the hero is". They still do.

Once you recognise it, you see it all the time. Snyder's example is Sea of Love, when Al Pacino's cop lets a petty criminal go free because he has his son with him. Another favourite is Disney's Aladdin, who gives his bread to some starving children even though he's hungry. He's a thief, but he's a good guy. In countless movies, though, characters literally save cats or pet dogs. Snyder's inspiration was apparently Sigourney Weaver in Alien, who considerately rescues the ship's cat (after half the crew have died trying to save it). Clint Eastwood randomly toys with a kitten for in The Good, the Bad and the Ugly, just as Frank Langella pets a nearby dachshund at his lowest point in Frost/Nixon. Will Smith refuses to shoot some lions in I Am Legend once he realises they have a cub (he also has a pet dog for good measure). And what's Marlon Brando doing in the opening scene of The Godfather? Petting a cat!

Which brings us to Inside Llewyn Davis. They could have called it Save the Cat: the Movie. Early on in the film, we see Oscar Isaac's hapless protagonist inadvertently let a ginger tom out of an apartment, and he spends much of the rest of the story trying to find the cat, finding the cat, taking the cat on the subway, losing the cat again, and so forth. Some have even suggested Llewyn Davis actually is the cat. It's not a bad theory: they're both charming drifters who survive on the hospitality of others and spread their seed irresponsibly. He's trying to save himself, see?

Another interpretation is that this is the Coens' riposte to the whole screenwriting-by-numbers game. So widespread has Snyder's formula become, he's often blamed for the predictable sameyness of commercial cinema – which has presumably been trying to replicate the success of Stop Or My Mom Will Shoot! all these years. But the Coens haven't exactly been above save-the-cat scenes in the past. Just a few years back in True Grit, Jeff Bridges saves the mule; when he finds two Native American kids abusing the creature, he kicks them off the porch and sets it free. There's a good one in No Country For Old Men, when Josh Brolin returns to give water to a dying bandit. We're on Bridges' side in The Big Lebowski from the moment he writes a cheque for 69 cents, and with George Clooney in O Brother, Where Art Thou? after he courteously inquires whether any of the hobos in the train carriage were "trained in the metallurgic arts before straitened circumstances forced you into a life of aimless wanderin'?" Inside Llewyn Davis is all the better for not playing by the rules. Instead it points them out, and tells us we shouldn't fall for them. The cat is out of the bag.