I agree, but unfortunately people have always tried to degrade the idea of women's rights by saying that it's anti-man.

So many women are all "oh no, I'm not a feminist, I love men!" and so many men think that women who stand up for their rights are just whiny bitches out to get them.

What she's saying is a bit reductive, but her essential point - that degrading and disempowering one half of the population makes things worse for the other half too - is very true. Women's rights are human rights, and anyone who doesn't grasp that might not take women's rights seriously.