Eh, I wouldn't say so. I think it's mainly because men are pushed to be more tough and much less expressive of emotions, which, for one, pushes them down those horrible alt right pipelines, but also makes it hard for them to feel intimacy and make meaningful relationships much harder.
I believe that gender norms incredibly hurt both men and women.
Damn right they do. Toxic masculinity means I can't publicly express myself without this look:
Edit: down votes. See what I mean? Fascism thrives off toxic masculinity. The Nazi beliefs were that a man's role was to make children to propagate the "correct" genes, and die in war. It's a chicken and the egg problem, and we can't address one without addressing the other.