I think there's a subtle pun in the title. Jim Stark (Dean), the "rebel", is seen by his parents and no doubt most adults (not quite all of them, it will turn out) as rebelling, going wild, getting into trouble, without cause. They view him as a kind of quantum accident. Most viewers will forget this by the end, but that's how we first see him, too: when he turns up at a police station one night, the very day he's been moved into a new town (yet again). By the end of his first day of school - after starting out determined to get things right this time - he's already been in a knife fight. But by now we see it's not because he's a poor character, nor because he's stupid. He's more than capable of redeeming himself if given the chance.

I'd heard that this was the first film to take teenagers seriously, without condescension, but I never expected that to be as true as it is. You start expecting an exploitation piece about juvenile delinquency with mounting violence and instead end up getting- well, best not to say whether it's something sweeter, more tragic, or perhaps both.