If we want to talk about harmful gender norms, we can find plenty that affect both men and women. I don't think there's any reason to assume that women are harmed more, especially when most of these gender norms are just two sides of the same coin (with one prominent problem being the fact that we all but ignore the side that affects men).

If we want to be consistent and honest, I think we need to look at this phenomenon where women are assumed to be the "bigger victims". Which itself is probably one of the biggest and most widely accepted gender norm in society. It's why we have a "women first" attitude pretty much everywhere, including in discussions about equality and gender norms. And it harms both men and women (and trans/non-binary people for that matter) in the real world.