@v_scarlotte_rose: underdog stories are almost never underdog stories when you look at the story. There is perceived underdogs that aren't really and those who are actually underdogs. Batwoman has literally no real chance to beat Batman on any level. Every stat that you can think to compare the two, Batman is superior. For it to be realistic for Batwoman to beat Batman it would require that she have something over him. She doesn't so she can't.
Stats might not be the only factor though. There's advantages either of them could have in the location they're in, clever use of gadgets, etc
Why would that be a thing? Perhaps you aren't aware of the world you are in, but showing women as inferior in any way generally leads to claims of misogyny, same with violence, same with many other things... It's not called out directly all the time, but the more in there the more likely it will be called out, no matter how much it isn't. This is the type of thinking that a lot of publishers, editors, and writers have and they think it will sell well so they do it.
I suppose some people might call it misogynistic if Batman wins, but I don't know if that would be fair, seeing as there's this notion of "Batman beats everyone".
It casts men as incompetent because it shows a man who has no way of actually being beat by this particular woman being beat by them. The only reasoning thus becomes "won because female" I'm not saying that her beating him under any circumstance would be misandrist... just just about anything they are likely going to write. And keep in mind I'm not saying this because of one incident of this type of stuff. It's all over the place, but people ignore it. They're blind to it because for them it's normal and when something is normal you stop seeing it.
Without knowing the circumstances of the fight, we don't actually know if she has no way of beating him.
Yes there are examples of both, without going through the issues just consider, that Kate's GF whom I always forget her name. When she was introduced she was Metropolis Commissioner... she was then reduced to Captain when she moved to Gotham... That makes sense. She was reduced to Lieutenant with Flashpoint... no reason for this. I would classify this as at least one instance of misogyny. Not extreme mind you but it's there.
Maggie Sawyer is her name. I don't think I could call this misogyny, as there isn't a clear indication that a demotion is anything to do with her sex/gender. Or is there?
On the other side, just count how many men who are not villains, enemies, portrayed well, etc. And I would guess there are probably less than 20 males in general in all 22 issues. This is not true when you look at male solo titles. You may think of excuses for it, but without getting into a more in depth talk and open analysis could one really say.
There aren't really many women who are portrayed well either though. Apart from Batwoman herself there's pretty much just Flamebird/Hawkfire, Maggie and Wonder Woman. Jacob is shown to be kind of flawed, but with her best interests at heart, and particularly supportive of Bette. Abbot was shown as a good guy, even sacrificing himself in the fight to save Gotham. And just last issue there's the Murder Of Crows who trained Batwoman, and now Hawkfire.
Plus, Killer Croc had a whole issue dedicated to him, and showed him to be a deep character, even doing some good in the end to protect the people he cares about. Even Mr. Freeze was shown as protecting Gotham.
And if the series was really so anti-men, wouldn't more of the villains be men?
I don't think the creators are misogynists/misandrists, but there is a lot of normalacy of this stuff and there is an apparent concerted effort to appeal to feminists and their accusations that is quite apparent with at least a few titles.
Feminism is about equality, so is there really a problem in a title appealing to feminists? And considering the lower number of female solo titles, and often less representation on teams, is it such a bad thing for a few titles to represent women well?
If you want more concrete examples I'd suggest instead of listening to me, simply look at the comics... or really anything around you... and think about what this stuff is saying about these genders from the presented information, both within that story and within the overall universe.