Simplicity said:
Because everyone was once a child, and children are people who deserve respect even if they can't always act like adults.
That doesn't grant them a free pass to any establishment their parents choose, any more than I have a right to demand entrance to a women-only gym.
I believe that that's the crux of my point. Because kids are kids, they cannot be relied on to not cause a disturbance. True, adults can't either, but the numbers are such that the vast majority of adults won't cause a disturbance, and a sizeable minority (if not an outright majority) of kids will if expected to sit through a film that's too adult for them for two hours.
And, in the right circumstances, it just takes on disturbance at the wrong time to ruin the whole. The example was given earlier of a man who was trying to propose to his girlfriend when a kid ruined the mood. Similarly, an outburst at just the wrong point in a film can destroy it for everyone, even if it is the only incident in the whole evening, and even if it is silenced almost immediately.
I see no good reason why cinemas cannot designate some showings as adult-only, and let the customer decide. But, the moment they do that, they have a barrage of complaints against them from parents determined to boycott all showings because their little angels are barred from some showings.
Why not bar cell phone users from restaurants?
Actually, I support the use of cell phone blockers in cinemas wholeheartedly. I'm torn on their use in restaurants, where the noise is less disruptive. However, I have no problem with their use, if the restaurant has a sign saying as much in a visible place. I might even favour such an establishment over one without.
Why not bar the ugly from bars?
Ugly people are routinely barred from nightclubs. The poor are routinely barred from many places, by virtue of the prices involved if in no other more overt way.