There is not one thing called "anime" for her to hate. She probably thinks of the stereotypical "big-eye" anime like Pokemon or the ecchi/hentai stuff like Tengou tenge.
Even if she hates anime, she'll be drawn into the story of Monster or Seirei No Moribito, and neither the stereotypical anime graphics or ecchi-factor will be there to get in the way of enjoying them.
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