It's one of those things I don't think is possible to be perfectly honest. I have heard some people say they hate anime for example, but their reasoning behind it never makes a whole lot of sense. So when you extend it to cartoons as a whole, I think it makes even less sense.
Don't like the art? Well, not all cartoons have the same art style, so this would mean you don't like art in general if you hate all cartoons, because it would mean you hate all art styles.
Don't like the stories? Well, guess that means you don't like books, shows, or movies either. The stories and genres for cartoons are just as vast as any media.
Basically every part of a cartoon you hate would imply you also hate something much larger. The only thing cartoons have that no other medium does not is animation (Although CG and visual effects in movies are not exactly cartoons and have to be animated to, but in a different manner). Hating animation though is sort of odd, and if it's not the animation part that you hate ... then chances are you do not hate cartoons, you just have yet to find one you like.
What happens more often than not is you decide you don't like something and so you never actually give it any chance. It's sort of like how a DC fan may hate Marvel, or a Playstation fan may hate xbox. It's all down to psychology. You hate it, because you say you do, but the reality is ... you wouldn't hate it if you where not so caught up in trying to hate it. There maybe certain aspects you don't like, but that applies to everyone.