I recently saw "Gone Girl" (spoiler alert!) and have been reading articles about the portrayal of its female antagonist, who is manipulative and psychotic. Some argue that this portrayal is problematic, since it plays into misogynistic stereotypes about women. In response, others argue that while such pernicious stereotypes do exist, it must surely be permissible to create a character who is both female and psychotic--indeed, to insist that this character type just can't exist would be sexist itself.
Both arguments seem plausible to me, but I'm not sure how to reconcile them. Yes, it's bad to perpetuate negative stereotypes. At the same time, we must have some freedom to create characters that exemplify such stereotypes. Women are sometimes psychotic--we should be able to write about that. But then it seems like we never have justification to criticize any fiction at all, since this kind of defense may always be invoked in any particular case.