Quitting is (to the extent the metaphor works at all) firing your employer, not your boss; these can sometimes be the same, but often your boss is, like you, an employee of your employer, not someone with whom you engage in a direct exchange that you can terminate.

If a line supervisor isn't given permission to terminate his subordinates' employment (because, e.g., that's reserved for a higher-level manager), but can quit, it would be wrong to say he can fire his employees. Likewise, it is wrong to say you can fire your boss unless you can terminate the boss's employment.