Critics were iffy on its release, but the icy tale of devoted sisters and its showstopping songs have won over children around the world. Recently, it looked as if Frozen’s icy dominion over our household was finally about to thaw. “I didn’t think it was possible to watch Frozen too many times but now I know every word,” said my seven-year-old daughter.

“Oh, do you want to stop watching it then?”

“No!”

Fair enough. Frozen-mania bypasses logic. It’s a compulsion. Friends have told me about their daughters playing the soundtrack on a loop, reliving the movie as they go; watching the DVD at least once a day; turning each bedtime into a climb up “the north mountain”; renaming their old toys Anna, Elsa and Olaf; loving it so much that they’ll even watch a dodgy download in Cantonese because they know the words anyway. One mother said there should be a support group, Frozen Anonymous.

It’s a rare thrill to watch a genuine pop-culture phenomenon unfold. At first, Frozen was simply the new Disney movie. Then it was a very good Disney movie. By the time it became the highest-grossing animated movie of all-time (overtaking Toy Story3) at the end of March, it was a generational touchstone. Over the Easter holidays, my daughter heard another girl singing Let It Go, Frozen’s centrepiece anthem, and they became instant friends, like two men at a barbeque realising that they support the same football team.

Colossal and cultish

My two-year-old is equally obsessed. Ironically for a film about the distance that can develop between sisters, Frozen is the one cultural artefact both my daughters can agree on. Like Star Wars, Grease or The Sound of Music, it’s somehow both colossal and cultish, the set text for a whole generation of girls (and a fair number of boys). Iron Man 3 may be one place above it in the list of all-time worldwide grosses but you don’t see hordes of boys dressed in plastic armour quoting Robert Downey Jr’s quips verbatim. For many children, Frozen is their first taste of full-blown fandom.

The numbers are mind-boggling. Directed by Chris Buck and Jennifer Lee, Frozen has grossed almost $1.2 billion (Dh4.4 billion) worldwide. It has won Oscars for best song and best animated feature, Disney Animation’s first since the category was introduced in 2002.

Disney’s official YouTube clip of Let It Go has racked up more than 223 million views; cover versions, mash-ups and parodies amount to hundreds of millions more. The soundtrack has topped the Billboard charts for 13 weeks and counting. Disney’s second-quarter net profit is up 27 per cent. A stage musical is in the works. A sequel is yet to be confirmed, but is as inevitable as the sunrise.

Disney made certain smart calculations. A musical is more rewatchable than a film without songs, and Frozen was the only family movie on offer during the holiday season, when cinemas were otherwise full of Oscar contenders. But it still drastically miscalculated demand.

Fans queuing to meet actors playing Anna and Elsa at Disney theme parks had to wait as long as six hours. “Word has it that those characters are like the Beatles now, attracting large crowds of screaming females,” reported Jezebel.

In a feeding frenzy on a par with Buzz Lightyear figures in 1996 and Cabbage Patch Kids in the 80s, all but the most unlovable items of merchandise sold out: even before the DVD release in March, Disney had sold half a million Anna and Elsa dolls.

In the Disney Store, parents have to enter a lottery just for the chance to buy the most desirable item, an Elsa costume. Limited-edition dolls and dresses have been selling on eBay for more than £1,000 (Dh6,177). Margita Thompson from Disney Consumer Products says in her defence: “Frozen is a global phenomenon that has truly exceeded expectations on every level,” which is corporate speak for “Bloody hell!”

If Disney underestimated Frozen, then so too did many of the critics. Variety called it “longer on striking visuals than on truly engaging or memorable characters”. The Onion AV Club overdosed on faint praise: “Frozen isn’t quite as accomplished as The Princess and the Frog, Wreck-It Ralph, or Tangled. But in its simple pleasures, it’s every bit as enjoyable as Winnie The Pooh.” In the spirit of the man who turned down the Beatles, the New York Daily News critic complained: “What’s crucially missing, however, is a hissable villain. Nor are there any memorable tunes.”

Fear and shame are villains

When Pixar releases a film about a cranky old man mourning his wife, or a rat that aspires to cook haute cuisine, or a post-apocalyptic robot trash collector, critics are primed to expect something different.

Frozen, at first glance, looks like more of the same. You get two big-eyed, wasp-waisted princesses, a square-jawed love interest and a wisecracking sidekick. One of the sisters, Anna (voiced by Kristen Bell), is spunky but naive, just like Rapunzel in Tangled or Merida in Brave. But the other one is Elsa (Idina Menzel), and she’s the movie’s X-factor. To complain that there isn’t a clear-cut villain is to miss the innovation that makes Frozen so fresh and resonant. The villains aren’t people but emotions: fear and shame.

A version of The Snow Queen had been trapped in development hell for decades. As far back as the 1940s, Disney had tried and failed to update Hans Christian Andersen’s dark fable. In the late 90s, off the back of the so-called Disney Renaissance (the creative rebirth running from The Little Mermaid to Tarzan), the company attempted it again and shelved it again.

In 2008, Chris Buck, a veteran animator and director of Tarzan, pitched it to John Lasseter, chief creative officer of Disney Animation, as a traditional hand-drawn animation called Anna and the Snow Queen, with Elsa as a villain trying to thwart Anna’s love for Prince Hans. That stalled, too, but bounced back as Frozen with Jennifer Lee (who wrote Wreck-It Ralph) as screenwriter and co-director, and some crucial twists.

The most successful animations have at their core a relationship threatened by a child growing up, whether it’s the neurotic helicopter parent and rebellious son in Finding Nemo, or the outgrown toys in Toy Story 3.

Frozen has the faultline between sisters. Once the film-makers decided that Anna and Elsa would be related, they called a “Sister Summit,” inviting female Disney employees to discuss their childhood relationships with their siblings. The sense of mystifying estrangement that a younger sibling can feel is summed up in Do You Want to Build a Snowman?: “We used to be best buddies and now we’re not/I wish you would tell me why.”

But if that were the whole story, then costumes for funny, quirky, approachable Anna would be the hot ticket. Instead, most girls are drawn to angry, conflicted Elsa: Disney’s first emo princess.

Some credit must go to Broadway duo Robert Lopez and Kristen Anderson-Lopez, who wrote the songs while the script was still in flux. It was the complex empathy of Let It Go (the couple said they were “thinking from an emo kind of place”) that led Lee to rewrite Elsa and therefore the whole movie. “Up until then, Elsa was pretty much a straightforward villain,” said Lee. “After that, she was much more complex, more interesting and sympathetic.”

Miscalculation

In an early miscalculation, before it saw sense and posted the Let It Go sequence on YouTube, Disney remade the song as a Katy Perry knock-off and gave it to pop star Demi Lovato. Her version flopped, not just because the arrangement and delivery hobbled the song but because fans didn’t want Lovato to sing it: they wanted Elsa.

In plot terms, we know that Elsa is deluded when she sings Let It Go. Her explosive liberation comes at the cost of lifelong solitude and, not that she realises it yet, eternal winter for her kingdom. But the song is so good at conveying the rush of reckless self-empowerment that it suspends our knowledge of the dire consequences for a few minutes. To Anderson-Lopez, the message of the song is: “Screw fear and shame, be yourself, be powerful.”

One of Marvel Comics’ great innovations in the 60s was to reframe superpowers as a metaphor for the chaos of adolescence. Like DC, Marvel had its share of aliens, gods and billionaire gearheads, but with Spider-Man and, especially, The X-Men, it introduced mixed-up teens whose powers were as much a curse as a blessing, and who had to contend with school bullies and unsympathetic parents as well as supervillains.

Within the constraints of big-eyed, wasp-waisted princesses and the need for old-fashioned charm, Frozen is progressive in a surprising number of ways. Playing with the viewer’s assumptions, it mocks the idea of love at first sight and the magical powers of “true love’s kiss”, making the handsome prince a “sociopathic” fraud and good-natured Kristoff a helper rather than a hero. It passes the Bechdel Test by having scenes in which women talk to each other about something other than men.

Its men are either devious or daft while its women are outspoken and powerful. With so many female-friendly innovations, you suspect that the role of comic-relief snowman Olaf was deliberately overstated in the first trailer so as to lure boys in as well.

Frozen is a landmark in industry terms, too: the first film with a female director to gross more than $1bn. Like The Hunger Games movies, it has triumphed at the box office with female leads, part of a long overdue shift addressed by Cate Blanchett at the Oscars when she taunted “those of us in the industry who are still foolishly clinging to the idea that female films with women at the centre are niche experiences. They’re not. Audiences want to see them, and in fact, they earn money.”

Feminist masterpiece

It might be over-egging the pudding to claim that an animated fairytale, however cheerfully subversive, is a feminist masterpiece. Anna and Elsa are still princesses and therefore part of the regressive “princess-mania” targeted by US writer Peggy Orenstein in her book Cinderella Ate My Daughter.

It will be a shame when the sisters are inducted into the think-pink mafia of the Disney Princesses, where they will have to hang out with drips such as Cinderella. But Frozen is still a leap in the right direction. One funny YouTube clip has Elsa scolding the other princesses (few of whom ever had to wrestle with the responsibilities of ruling, let alone uncontrollable superpowers) for their passivity: “Why keep on assuming men can save the day?/I can be the hero and I can do it my own way.”

Frozen is likely to be a transformative movie for both Disney and women in Hollywood but the industry story somehow feels less interesting than the drama that’s taking place in millions of homes.

My daughters aren’t memorising Disney’s second-quarter net profit figures. They’re being swept up in an obsession that, echoing my own childhood fixations, feels both communal and deeply personal. Better still, the object of the obsession has powerful things to say about sisterhood, storytelling, adolescence and female autonomy.

This movie will be a major event in my children’s memories of 2014 and therefore in mine too. I may have heard these songs countless times but I’ll miss them when they’re gone.