The Mark Zuckerberg of David Fincher's masterful film is angry, lonely, vindictive and vengeful. He's the classic outsider looking in, an unlikable anti-hero with only one redeeming feature – a superb brain. He's a variation on Tyler Durden, the central character of Fincher's Fight Club, with just a shade of Kevin Spacey's John Doe from Fincher's earlier Se7en. As played so brilliantly by Jesse Eisenberg, this Zuckerberg simply doesn't like people much. How ironic, then, that he should end up, as another poster for the film puts it, with 500 million friends.

As a student at Harvard, the movie's Zuckerberg is surrounded by real-world social networks – the sororities; the old-money WASPs; the jocks; the ravers – but they're all clubs to which he would never want to belong, which is lucky as they'd never have him anyway. He looks at them with a toxic mix of disdain and envy.

He stumbles upon the idea for his site because he's furious at the girl (Erica Albright, played by Rooney Mara) who's just dumped him. He takes the idea further, to what eventually becomes Facebook, not because he wants to be on the inside, but because he despises all those who already are. It's a giant "f--- you" to all the gatekeepers of all the clubs, adolescent and adult alike. It's Columbine in code.

How much of this depiction is accurate is hard to say – Aaron Sorkin, who wrote the incredibly wordy but never dull script, happily admits there's a heavy dash of invention in it – but there's something wonderfully appealing in the idea that the world's greatest social networking tool just might have been created by one of the world's greatest misanthropes.

In fact, it's hard not to feel some sympathy for Zuckerberg's worldview. Though hardly a poor scholarship kid, he's mixing it at Harvard with those whose greatest attributes are kind genes and a healthy trust account, and when he burns those who dare to patronise him or try to hitch a free ride, it's only knowing how rich and powerful and (in some eyes) exploitative the real Zuckerberg becomes that might undermine your cheerleading.

The film is largely built around two legal cases. One is brought against Zuckerberg by the Winkelvoss twins, Cameron and Tyler, played in an amazing feat of CGI wizardry by the one actor, Armie Hammer, and their partner Divya Narendra (Max Minghella). The trio claim they hired him to write the code for a site spookily like the one he first unleashes as TheFacebook in early 2004, at which time he was meant to be building theirs. In other words, he stole their idea.

The other case is brought against Zuckerberg by his former roommate and best friend, Eduardo Saverin (Andrew Garfield), who claimed that Zuckerberg (or, rather, lawyers acting for him) had swindled him out of his share of the company he co-founded when it started to take off.

Both cases are real. Both have been settled, with Zuckerberg paying the Winkelvosses in shares and cash to the value of a reported $65 million (though they are apparently suing again on the basis that Facebook misled them as to the true value of those shares). Saverin had some of his shareholding reinstated, and his name once again appears on the Facebook corporate page as a co-founder.

A bunch of spoilt brats sitting around a table arguing about who did what, when may sound dull but it's not. Zuckerberg is a powerful if impolitic figure, oozing contempt for inherited wealth and soft minds, who wields the withering put-down with Wildean relish. He's smart, he knows it, and he wants everyone else to know it too.

The only hint of an actual connection with a real human being comes when Zuckerberg meets Sean Parker (Justin Timberlake), a co-founder of Napster, a man who mixes his own misanthropy with a massive dash of charm. In a key scene, Parker confesses to Zuckerberg that he was motivated to start Napster after being dumped by a girl for a footballer back in high school. Parker is playing Zuckerberg like a pawn, but the younger man's face lights up all the same. Yes, at last, he seems to say; someone who understands me and my rage.

The real Zuckerberg recently donated $100 million to the state school system in New Jersey. Cynics immediately read it as a pre-emptive PR stunt, designed to offset the negativity he feared the film would generate. He needn't have worried so much. He may not come across as likable, but neither does anyone else (except, perhaps, the girl who dumps him). But he sure as hell comes across as smart, determined and, ultimately, right.

Of course, the way the film has it may not be the way it happened in the real world. But then the real world is hardly the point, is it?