Many feminists actually do talk about "sorority" in that sense of women helping each other, however, many other feminists don't agree with that. First reason is that this would block criticism within feminism, such as the one made in the post.
Second reason is that women aren't all equal, women don't all have the same problems, so if feminism embraces the sorority concept, it would lead to minorities' issues just getting ignored, i.e. no one would care about autistic women. So, it's not that feminism isn't for women, but women do have their differences and they need to deal with that.
Lastly, feminism isn't about being against men. Sure, some radical feminists are against men, but I don't think they're taken seriously. Actually, there is a debate among feminists about whether men should or not be allowed to engage in feminism, and there are plenty who think they should. How can you expect men to help in feminism if feminism is against them? You can't, so that's not the case.
[Edit: removed a line I thought it wasn't polite 10 minutes after posting.]