With how the site is, now's a good a time as ever, right?
Recently met up with and had a conversation with an old acquaintance (who I respect in some ways more than others), noticed a few things.
It is easy for a man to have contempt for what culture and society claims are the follies of women: they are emotional, they do not know what they want, they play mindgames, they are petty. A woman's anger is considered hysterical. A woman's interest in fashion is a mark of her vapidity. A woman without a father has "daddy issues." These are reinforced and internalized over and over again, from an essentialist view, as 'irrational' behavior.
But when a man does not know what he wants, it is "him finding himself." When a man plays mindgames, he is smart and devious and a "magnificent bastard." When a man is petty and one-ups someone, it is an "alpha move." A man's anger is considered to be just, righteous, and awe-inspiring. A man's interest in fashion is a mark of his class. A man without a father is a noble tragedy.
People hate in others what they hate in themselves, as they say.
When girls write love letters to murderers in prison, society gasps collectively. How dare they! But when boys commit murder, we shrug and say... why wouldn't they?
It's easy to say you're a feminist or ally or whatever you want. But remember the society you came from sank its hooks in deep, and its fallacious appeals to nature ("Women just want to be mothers, and this is clear by how we pressure them to be mothers!") are persistent. Remember a lot of psychological and sociological research was performed on specific populations that aren't universally representative. Remember that sexual dimorphism and differences in brain structure are not the end-all. Don't ever stop being self-critical.
One of the rightists' greatest weaknesses is their inability to see the potential in half of the world population. Women hold up half the sky, and you're doomed to failure if you entertain ideas to the contrary.
It's not just "good," if we look at more media. If a woman is an active driver of events, rather than a passive observer, she is going to be held to a higher standard and scrutinized more closely because she is actively defying cultural norms.
You can see this whenever women pirates or women warriors are brought up: suddenly, rightists care very deeply about how immoral it is to be a pirate, or the war crimes committed by people in Medieval times. The kind of things that they would either ignore or celebrate if it was a man doing it.
You can see this in how the term Mary Sue is (mis)applied. It describes an actual problem (characters who are so invincible and perfect that they're boring), but if you look at which characters are actually described as Mary Sues, the threshold for women tends to be much lower than the threshold for men.
I believe that's at least in part because it started out as a fanfic term to describe a self-insert who functioned like a black hole (derailing plots and upstaging characters, etc) and then later made the jump to just generically referring to boringly overpowered characters. However, I still agree with your overall point - particularly given how that that is how the term is used now, it is especially egregious that female characters get the extra scrutiny since there have to be at least ten Marty/Gary Stus for every Mary Sue in pop culture, at least by my reckoning.