Your comment reads to me like you're saying that you're okay with believing in stereotypes about women [and men], and that you don't see any problem with maintaining rigid gender roles. This to me, is
not congruous with the statement that you believe in equality.
> The problem is, you can't understand someone over the internet.
This is true, and that's why one should go out of their way to be welcoming to all-comers when promoting an event like this. There are things you can say to your friends that are not appropriate to say in a professional or more-public setting, because people have no way of knowing whether you're joking or just an asshole.
> Do I believe a woman should be able to do whatever the fuck she wants in this world, be it fighting fires or curing AIDS? Yes.
One of the things that would prevent your sister from doing that is misogynistic cultures in the [fire/AIDS/bug]-fighting community. Who wants to pursue a career in an environment where they're not welcome, or treated as second-class citizens? This is the reason people are reacting so strongly to this.
> For the most part men and women are aware of their stereotypical flaws. Search for "Shit girls say" on youtube and admire the view count. I don't know a single girl who didn't completely piss her pants watching that.
The thing is, not all men and women have the same flaws. Stereotypes tell us they do, but that isn't true. And there are plenty of people [1] who thought shit girls say was sexist (including me.) The reason I think it's sexist is because it portrays basically one way for women to be, and perpetuates the idea (while not outright saying it) that all women are like that.
[1]: https://www.google.com/search?q=%22shit+girls+say%22+sexist