I’ve been meaning to answer this for a while now. I do think it goes both ways, but my personal experience and a few thorough studies show that men are more confident than women; that’s it’s easier for them to stand their ground and get respect. At the same time, women tend to be more self-critical and blame themselves when something isn’t working.
That’s why I find it important to remind women specifically of their worth.
That being said, gender doesn’t matter: we’re all human, we all deserve to be treated the way we treat others.