I don't think it should. To me, Feminism is the view that society prioritizes the views of men over women and that women suffer injustice as a consequence. Feminism's solution to the problem of gender inequality is the advocacy of women's rights and the awareness of women's issues. While a feminist may genuinely care about men's rights, Feminism does not, nor should it. Feminism is simply not about men. That's why we need men's rights too. Feminists who care about men's rights should try to separate those issues that are legitimate from those that are anti-feminist (you know, manosphere stuff like incels and MGTOW). I know men's rights groups don't make it easy. However, in my opinion, some of their concerns have merit.