Sexism is typically defined as “attitudes or behavior based on traditional stereotypes of sexual roles” or “discrimination or devaluation based on a person’s sex.” Sexism is a gender-neutral term, not based on “power plus oppression” like some people on Tumblr apparently believe.
Yes, you can be sexist toward men - they do experience harassment and sexism. Sexism against men is almost institutionalized in the USA with biased legislation such as VAWA, which primarily criminalizes men (via the Duluth Model) despite the fact that women commit just as much (if not more) domestic abuse as men. Female mass murderers (2) also exist and some murdered for fun or other similar reasons (many perpetrators of mass violence are mentally ill). They also commit other crimes yet recieve shorter sentences than men. The CDC reports that in cases of non-reciprocal intimate partner violence (one directional), women are more than twice as likely to be the aggressor. The report cites that women comprise 70% of perpetrators, while men are a mere 30%. Instead of calling attention to this fact and promoting gender equality, feminist publications such as Jezebel make fun of female-on-male abuse. As it is, men are already unlikely to report their abuse; they don't need feminists making fun of them for it.
Swedish feminists have moved to ban all criticism of feminism, ban men from standing to pee, ban plows from plowing snow in certain ways, and other silly things which have nothing at all to do with gender equality. Which for some reason includes kidnapping women. In some countries, men are not allowed to get paternity tests or heavy restrictions are placed upon the testing criteria. In the USA, gun violence revolving around men is a highly misunderstood issue.
While many feminists are trying to do good, others are not. At all. Feminists shut down forum for battered husbands. Feminists blame males for their own abuse. Feminists dismiss female child rapists. Feminists say men can’t talk about domestic abuse. Feminist Mary Koss denies male rape victims. Feminists say men can’t be raped. Man raped and forced to pay child support. Feminists defend female raping minor. Feminist defends why raping an 8 year old isn’t rape. Defining male rape victims out of existence. Feminists primary aggressor clause discriminates against males. Women commit domestic violence as often as men... but only men get arrested for it. Feminists cover up female domestic abuse stats. Woman smashing bottle in mans face in public. Nobody seems to care. Feminist site mocks men who are abused. Female on male abuse in public is at best ignored, and at worst celebrated. Public stops a man from abusing a woman in public, same crowd laughs when the roles are reversed. No funding for male shelter. Hotlines refuse to help men. Founder of Canada's only male shelter for abuse forced to close due to lack of funding before committing suicide. Female abusers ignored.
Misogyny exists and misandry exists, as they’re simply more aggressive forms of sexism and both genders can exhibit sexist behaviors and attitudes. Both may not have the same effect in a societal context (misogyny tends to be worse in most situations) but they do exist regardless. However, western society is not misogynistic (as feminists often claim).
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