If there are two things I don't understand with fandoms it's when:
1) People say "so-and-so doesn't get enough love" or "this character could use more attention" when it's actually one of the most popular characters in the fandom and you can find at least six billion pieces of fanart or material related to said character by doing one search alone.
2) People think they're "special" or "just weird like that ^__^" for liking 'psycho' characters. The "lol yea im sort of different becuz my fetish is crazy guys/chicks/characters and i guess that makes me strange lolol xD" variety.
Because seeing at least ten million characters, original or established, with the same 'tude grin, blood-covered mouth, goffick or scene attire, and "i-will-lick-this-bloody-knife-to-show-how-hardcore-i-am" generic anime "crazy person" pose is something you'd never find in a million years.
Actually, no. I do understand. I just think it's dumb.
That is all.
Edit: To prevent misunderstanding, that's not to say there are no "good" or "well-done" insane characters or that it's necessarily a bad thing to like them (I've liked a few myself). But to assume that it's a "rare" or "unique" thing to like them is just silly.
Edit: Since some also touched on this, people who use both 1) and 2) to gain attention or sympathy. Ex. "this character doesn't get enough love and im rly sad about it guys" when doing a search actually shows that their post is embedded within mountains of fanart or posts related to said character.
Edit: To add to the "insanity" thing, I don't think that every insane fictional character always has to have an illness that matches a real-life one 100 percent, but I do believe some creators/characters develop or flesh-out events or circumstances that lead up to the 'breakdown' better than others.