Because nobody likes playing with cheaters.
Playing games should be fun. In order to ensure the best possible online multiplayer experience, Valve allows developers to implement their own systems that detect and permanently ban any disruptive players, such as those using cheats.
Game developers inform Valve when a disruptive player has been detected in their game, and Valve applies the game ban to the account. The game developer is solely responsible for the decision to apply a game ban. Valve only enforces the game ban as instructed by the game developer.
For more information about a game ban in a specific game, please contact the developer of that game.