There may be one big reason why some females in the states and Europe aren't too into anime, and it has something to do with the portrayal of women. As I've said many times before, things are quite different in Japan than they are in the rest of the world. Some of the ideas put forth by the Japanese people aren't exactly too popular elsewhere. A majority of anime seems to take those ideas and run wild with them, leaving women in the rest of the world feeling a bit uneasy.
First off, there are plenty of anime where women are objectified. Yes, we've all see the strong anime female before, but she's usually running around in next to nothing. Most anime take every chance they get to show a little fan service, and while I can't say that I dislike it, I can definitely see how some women would take offense with it. Showing girls as something to drool over and nothing else isn't exactly the best way to get on a lady's good side.
Then there are the female anime characters that do nothing but cater to a man's every whim. That might be a husband, boyfriend or crush, but they all get treated the same. Some female anime characters go out of their way to be polite to the male characters, never questioning what they have to say. It's all about keeping the man happy and hiding away personal opinions. Again, this doesn't really fall in step with the rest of the world, and I can definitely see why women might be a bit upset with it.
How do you feel about the portrayal of females in anime? There are some features that show us strong, proud female roles, and those are the ones I really dig. When women are used as sex objects or vapid bodies in anime, I can see where the real-world counterparts get a bit ticked off. I'm not against fan service in any way, but anime that uses women for this purpose only is doing nothing but hurting its audience.