bear in mind if it had splitscreen, the game would have to render the entire map, characters, guns, and everything else twice, which would hurt whatever system you use with todays complex graphics systems. That's the reason why so little games have split screen these days, and the reason why hardly any sandbox games have ever had it.
It's disappointing, but I understand it.
To elaborate on this, there's a specific technical reason that splitscreen doesn't work in Brink specifically. Splash Damage has said they've developed an engine that wastes fewer resources on graphics that aren't going to be rendered on screen, so that the game can be more visually impressive without requiring more hardware. Having two players on the same system doesn't just mean having two cameras in the environment, like it might in other games, but actually storing more of the environment in memory, which means the game would slower (or be uglier) by a wider margin than other games would.