I’d better come clean right away: I am a Frozen fan. And not because I have small children whose obsession forced me to choose between insanity and just getting the hell on board. In fact, it was me who spent the months after the film’s release recommending it to everyone’s kids (you’re welcome, friends).

I hasten to add that I’m not crazy. I haven’t made a YouTube cover of Let it Go; I don’t have a white-blonde wig. I just think it’s brilliant. So while part of me wants to answer with the words of the woman who allegedly divorced her husband for Frozen ambivalence – “If you can’t understand what makes this movie great, there’s something wrong with you as a human being!” – I do understand people’s bafflement. Because, even to a fan, the film’s cultural domination defies belief.

Since its release in December 2013, Frozen has become the biggest animated film of all time, grossing over $1.2bn globally. It won two Oscars (best original song and best animated feature film), a Golden Globe and a Bafta, and is currently the UK’s bestselling DVD of the decade. Its multi-platinum soundtrack beat Beyoncé’s surprise fifth album to the top of the Billboard charts, and the official singalong YouTube video of Oscar-winning Let it Go has had more than 940m views. The film’s merchandise consistently tops “hottest toys” lists, a Broadway show is in the works, and when Frozen 2 was announced last March, Disney’s stocks jumped $4.28 in a day.

So what is all the fuss about? Well first there’s the writing, which has been roundly praised for its nuanced characterisation, multi-generational comedy, delicately shifting tone and perfect plot arc. As one unfeasibly perceptive six-year-old told me: “It’s got that same story that’s in every film: you get to know the characters, then the story starts, then there’s a problem, then it gets sorted out and there’s a happy ending.” The classic hero’s journey, comfortingly familiar even before we understand what it is. But this one comes with twists on the usual Disney template, and it is these twists that form the basis of the world’s obsession.

Frozen has not one, but two Disney princesses, and neither of them fits the typical mould; the customary love-at-first-sight royal engagement is ridiculed; the handsome prince is a bad egg; and the finale ditches romance for sisterly devotion. Rescues are at the hands of the spunky, younger princess Anna – something her sidekick Kristoff accepts without a single grumble or mansplain. There’s even a same-sex couple with a gaggle of giggling children.

Such progressive elements not only sparked hefty debate and hearty praise from critics, academics, parents, and equal rights campaigners – helping to fan the flames of the film’s populist blaze and rack up the box office sales (after all, it’s not kids but approving adults who buy the tickets) – they also delighted children.

‘Perhaps that’s the film’s real power; the fact that we just can’t stop talking about it.‘ Photograph: Allstar/Disney/Sportsphoto Ltd

My six-year-old correspondent listed many reasons she and her friends love Frozen, and most of them tallied with those of the adults. The fact that “girls can be heroes, too. Not just boys”; that “you can choose whether you trust someone and it’s OK if you don’t” (the Prince Hans lesson); that it’s “OK to be yourself” and that “if you do something by accident, like get angry, that’s OK, because you probably didn’t mean to”. The last two are the Elsa lessons and, if there was one character who could be credited with sole responsibility for Frozen’s success, it’s her.

The complex, damaged older sister with icy powers that her abusive parents forced her to conceal, was originally the villain of the piece – blue of skin and spiky of hair. But when married songwriting duo Robert Lopez and Kristen Anderson-Lopez composed Let it Go as an empowering ode to self-acceptance, the film was rewritten and Elsa-mania was born. Voiced by Idina Menzel, she’s undoubtedly the darling of the film’s younger viewers; the combination of her powers and how she reacts to them enchants the target audience. But her anthem – which Anderson-Lopez says should encourage people to “screw fear and shame, be yourself, be powerful” – became a touchstone for a huge cross-section of adults, too. People feeling ostracised by society; cancer survivors; divorcees – messages of thanks flooded into the film’s creators.

And the Let it Go tributes began. Thousands of them, posted on YouTube by adults and children alike, winning millions of views. These were quickly followed by lip synchs and spoofs of the rest of the soundtrack. Which brings us to another force behind Frozen’s, ahem, snowballing popularity: social media.

This was the first big Disney musical animation to hit screens when its fans were old enough to take to YouTube, Twitter et al and share their fandom. Soon, elaborate fan art took over Tumblr and hundreds of hashtags sprang up – #thecoldneverbotheredmeanyway for the self-empowerment contingent and, more recently, #GiveElsaaGirlfriend, for those keen to see Disney’s first lesbian character in the sequel. And the fan debates aren’t slowing down; last year, Frozen was the most discussed film on Facebook. Two years after its release.

Perhaps that’s the film’s real power; the fact that we just can’t stop talking about it. You’re still Googling, I’m still extolling its virtues, academics are still dissecting its meanings and messages. Last May, the University of East Anglia hosted Symfrozium, the world’s first academic conference devoted to the film. There were presentations on Frozen’s fairytale roots, its reworking of the superhero genre, and its presentation of gender roles. And while some of the theories were less than favourable – one speech explored links between the film and pro-anorexia websites – most were full of praise for its trailblazing liberal outlook.

If you ask me, it’s that liberal outlook that’s keeping Frozen at the top of the DVD charts and the front of people’s minds. Because it gives us hope – and boy do we need that this year. If a cultural influencer as crucial as Disney is writing female heroes, promoting self-acceptance and tolerance, and positively representing same-sex parenting, then maybe, just maybe, the next generation will continue its good work in their own lives. Why is Frozen so popular? Because it represents the future that so many of us want.