Sadness, anger, fear, disgust - and joy: How Pixar, Mad Max and Hollywood's gender gap put us back in touch with our emotions in 2015.

If you wanted an encounter with life's soul-spinning complexities in 2015, all you had to do was watch a cartoon. This has been a great year for film, but it was a vintage one for animation.

More than six months after I first saw it, Inside Out still makes me stop in the street. Who on earth would think to explore the strange interplay of our emotions across a wildly imagined, metaphorical mental landscape, through a story about an 11-year-old child moving house?

The answer, of course, is Pixar - which, in doing so, reached higher and further than the studio has ever done in its 29-year history. With razor-edged emotional acuity, Inside Out reminds you that joy and sadness aren't mental rivals, but cohabitants - and to make that idea easily comprehensible to adults, let alone eight-year-olds, must be the single greatest storytelling achievement of 2015.

Amazingly, though, it wasn't an outlier. In March came The Tale of the Princess Kaguya, the final film from Isao Takahata - the lesser-known co-founder of Hayao Miyazaki's beloved Studio Ghibli. Freely adapted from a 10th-century Japanese folktale about a couple who find a tiny girl inside a stalk of bamboo, the film showcases Ghibli's mastery of the hand-drawn animated form.

Any year with new work from Pixar, Ghibli, Disney (with Big Hero 6) and Aardman (which produced the uproarious harlequinade of Shaun the Sheep) was likely to be a memorable one. But 2015 added a new name to the pantheon. The Irish studio Cartoon Saloon, founded by Tomm Moore and Paul Young in 1999, released its second fully independent feature in the UK, and marked itself as a world-class talent.

Moore's Song of the Sea follows a young brother and sister as they come to terms with the loss of their mother, one of the seal-folk, who has slipped away under the waves. As a bereavement allegory, it is acutely perceptive - and its hand-drawn artwork would have been impossible to realise in CGI, let alone live-action.

So it's fair to say that in 2015, children's films were more daring, inspiring and profound than most of the ones aimed at adults. And, happily, that doesn't seem to have proven a commercial stumbling block. Inside Out was Pixar's most successful non-sequel, landing in sixth place in the UK's annual box-office chart with £39.6?million.

In fact, even before the release next week of Star Wars: The Force Awakens, 2015 is already the most successful year for film in the UK to date. Box-office takings passed £1?billion on October 27, the day after Spectre arrived in cinemas.

With due respect to Fast & Furious 7's unexpectedly moving finale, in which the franchise bade farewell to its departed star Paul Walker, none of those films was as profound as Inside Out. But this has been a year in which profundity turned up in unexpected places.

I'm thinking particularly of Robert Zemeckis's The Walk, an apparently innocuous 3D thrill-ride about the high-wire walker Philippe Petit and his bold, insane, illegal 1,630ft journey between the roofs of the north and south towers of the World Trade Centre in New York City on August 7 1974.

Yet The Walk was one of the year's notable box-office failures: it made £27.5?million worldwide, a far cry from the £448?million Zemeckis's Forrest Gump took 21 years ago. If you caught it, you shared one of the vital big-screen experiences of 2015.

The most surprisingly profound film of 2015, though, was the year's most pleasant shock full stop - although "pleasant" is admittedly an odd word to use for a film in which the climactic fight scene involves the antagonist's windpipe being wrenched out of his mouth, then getting tangled around the axle of his own monster truck.

I speak not of The Lady in the Van, but of Mad Max: Fury Road, which arrived with a bang in mid-May and has been ringing in my ears ever since. It's a film that manages to be two hours of nothing but chase, yet simultaneously crams in more subtext about gender, patriarchy and the politics of control than 15 sociology degrees. What's more, it gave us Imperator Furiosa, an immediately iconic warrior-woman played by Charlize Theron with cropped hair, war paint, metal prosthetic arm, and a horizon-scouring stare for the ages.

Partly thanks to Theron, 2015 felt like the year Hollywood finally started to get over the wearisome tokenism of the Strong Female Character. Even more seismically, it finally began to come to terms with the gender imbalance that seems baked into the industry.

The 2014 Sony email hack, which revealed (among other things) that Jennifer Lawrence and Amy Adams had been paid considerably less than their male co-stars in American Hustle, led to Lawrence writing a blistering essay about Hollywood sexism: "I'm over trying to find the 'adorable' way to state my opinion and still be likeable," she wrote - which made me like her even more.

Behind the cameras, the prognosis remained dire. Of the 100 most popular films in the UK this year, only six were either directed or co-directed by women. But in front of them, things were noticeably brighter. Theron's Furiosa led a rush of intricately drawn screen women, who were every bit as eccentric, complicated, flawed - and, yes, compellingly weak - as men.

In The Diary of a Teenage Girl, 15-year-old Minnie Goetze, played by the terrific young British actress Bel Powley, decides to lose her virginity by seducing her mother's 35-year-old boyfriend. The fallout is confusing, with no clean-cut moral: the ideal conditions for riveting drama. The BBFC's decision to give the film an 18 certificate - in my view, wholly unmerited - meant the audience that would most benefit from seeing this story told thoughtfully and honestly were legally prevented from seeing it.

Cate Blanchett gave the best performance of her career in Todd Haynes's Carol, while in Olivier Assayas's Clouds of Sils Maria, a phenomenal turn from Kristen Stewart, as a cool-headed PA, suggested the young Twilight alumna was just getting started.

In short, there was much to be grateful for. But were we? In April, after I saw Avengers: Age of Ultron, my editor emailed to ask if anything newsworthy happened in the film. In my reply, I described a scene in which Scarlett Johansson's Black Widow reveals to Mark Ruffalo's Bruce Banner that she was forcibly sterilised during her training, before adding: "You still think you're the only monster on the team?"

"It's the kind of line that, taken out of context, could cause people to strop on social media," I wrote. "Twitter mobs have rallied around less." A couple of weeks later, that wasn't the half of it. A whining campaign by some Avengers fans claimed the line was misogynist. Director Joss Whedon, the thinking ran, must believe that infertility is monstrous, and that female characters are only interesting in terms of their capacity to reproduce.

This is an absurd misreading of the film. But the fuss suggested that the regrettably burgeoning "safe space" mindset - where even the mildest references to uncomfortable subject matter must be wiped away - is starting to have an impact on mainstream film culture.

We should be careful what we wish for. Cinema is never more exciting than when it challenges us - and studios, wary of the impact on their bottom line too many hashtag protests might entail, will sooner lose their nerve than a profit. So in 2016, let's cherish film's ability to make us feel everything: sadness, fear, disgust and anger as well as joy. Together in the dark is the best possible way to face our demons. The movies must continue to be an unsafe space.

The Daily Telegraph