Yeah, it's pretty clear we live in a very sexist society. I think when people who aren't exposed to gender equality movements much hear that they think it's a claim of rabid misogyny. It's not that though, most people aren't frothing at the mouth to say how shit women are (although we have a particularly nasty problem with domestic violence which is quite violent), it manifests in ways such as:

• finding women more annoying than men exhibiting the same behaviour
• speaking over women without even noticing they've talked
• requiring higher standards of evidence for statements made by women
• not actively seeking out the opinions of women in conversation in favour of giving attention to men
• demanding women adopt masculine mannerisms and socialisation to be taken seriously

It catches men in the crossfire too, men who fail to meet masculine standards are discounted. Think about short men, or men with higher pitched soft voices etc.

It's frustrating and why it's not enough to just try not be sexist, but to be specifically anti sexist. That is, to make a point of compensating for biases you probably don't want to express but were likely conditioned into expressing as a child in order to approach something more like truly fair treatment.