The difference between how misogyny and misandry is defined:

A man calling women names = misogyny. A woman calling men names = not misandry.

A man insulting a woman based on her looks or anything which is widely undesirable to men = misogyny. A woman insulting a man based on his looks or anything which is widely undesirable to women = not misandry.

A man inflicting violence on a woman = misogyny. A woman inflicting violence on a man = not misandry.

A man ridiculing women because they have feminist inspired beliefs = misogyny. A woman ridiculing a man because he has inspired beliefs on the rights for men = not misandry.

A male anti feminist = misogynist. A female anti MRA = not misandrist.

Disagreeing with a female centered point of view = misogyny. Disagreeing with a male centered point of view = not misandry.

A male being pro male = misogyny. A female being pro female = not misandry.

An MRA = misogynist. A feminist = not misandrist.

A man complaining about anything women generally do unfair or wrong = misogynist. A woman complaining about anything men generally do unfair or wrong = not misandrist.

Trying to shut down events, conferences, or a voice in general for women's rights groups = misogyny. Trying to shut down events, conferences, or a voice in general for men's rights groups = not misandry.

Objectifying women = misogyny. Objectifying men = not misandry.

Sexually harassing women = misogyny. Sexually harassing men = not misandry.

Being annoyed with a female being a CEO/PM/president = misogyny. Being annoyed with a male being a CEO/PM/president = not misandry.

Saying that men are better than women at doing things = misogyny. Saying that women are better than men at doing things = not misandry.

Men seeking traditional male privileges = misogyny. Women seeking traditional female privileges = not misandry.

Blaming women on anything = misogyny. Blaming men on anything, like using patriarchy as a multi purpose scapegoat for all the woes in the world = not misandry.

Which gender is beaten-up the most? By whom? How often?

Sure, it's genetic, and traditional. Guys got ahead by beating up other guys. They got laid by abducting women. They kept their women in line by beating them. That worked for a few million years of primate evolution, so it must be a racial survival mechanism. Damn biology...

But if a woman calls a man an asshole, maybe he *is* one.

So things that some men do, all men must be shamed. Things that some women do, it's wrong to shame all women as it would be considered as misogyny.

As always, lets just sweep it all under the rug when the facts are there that women beat up men and other women, rape, etc etc (insert any evil a man has done) too.

You may want to consider looking up the domestic violence rate on lesbian relationships compared to heterosexual relationships. There's a hint.