Let me tell you what sexism means nowadays: saying or doing anything that makes a woman that is concerned with gender equality feel uncomfortable at all, even if it has nothing to do with sexism, discrimination, or even your own gender. It's maddening.
What's important to realise is that we live in a society that is inherently sexist (that much is clear simply from the statistics), without really having many 'sexists' in it as you would normally define them. Nobody walks around saying (or even thinking, I suspect) that they hate women. The only sensible conclusion is that the bias is a product of our inherent subconscious prejudices, and unfortunately that's really hard to combat because it means we have to inspect every part of our behaviour to try to make sure we're not doing something that puts minorities at any more of a disadvantage.
I'm not defending the really extreme feminists who can definitely go way overboard, but I can understand where they're coming from -- how else do you fight this institutionalised bias that puts you at a significant disadvantage for your entire life? I don't think anyone has a great answer right now, and that has to be so frustrating. As a white male who's never faced much discrimination, it took me a very long time to empathise with that, but I think it's important.
