The rich culture and history of Japan and it's people. While it should be loved and respected, it should not be obsessed with and worshiped, as many American Anime fans do today. Many of the said fans will claim to know everything about Japan and it's history simply because they watched an Anime. Usually Anime/Manga is the only thing they really like about Japan. If you are Japanese (like myself), many of these fans will come up to you and randomly say words from the Japanese language and expect you to be impressed. They will also expect every Japanese person to be as in love with anime as they are, and will hate you if you simply say you don't care for anime.
Anime Fan: Hey! Did you watch (Insert Anime here)? It's so awesome! Because I've watched it, I know everything about Japanese Culture! Plus, (Insert random character here) is so hot!
Me: No, Honestly I don't care for Anime. And Frankly, I don't find fictional characters attractive, given the fact that they're fictional.
Anime Fan: But you're Japanese! You have to like Anime!
me: Well, I don't.
Anime Fan: You Hater! I thought you were Baka, but I was wrong!
me: *Rolls eyes*