I find that the three things feminists do not say at all (1, 3, 4) are often perpetuated by people who do not identify as feminists. It is most often women who indulge internalized misogyny and men and non-binary people who indulge in misogyny who say that all men are motivated by sex and violence to the point of destruction. As its corollary, heterosexual relationships are necessary because the gentle gatekeeper that is all women will keep these men in check. (Or, in other radfem cases, all men are a lost cause so political lesbianism is where it’s at)
To address how these are each problematic and why feminists never say them:
1. “If women ran the world, it would be more peaceful” Putting women on a pedestal of being the ultimate peacekeepers like this is perpetuating misogyny because it plays into established gender roles of all women as maternal and incapable/not prone to violence. Do you know women who love guns? I know a whole bunch of them. I know a whole ton of women who think the Iraq war was justified. Ironically, these are also a lot of the women whom I have heard say this.
2. “Government must ensure that women earn as much as men” but only if they’re doing the same job. This person seems to imply that feminists think receptionists (a job dominated by women) should make the same amount as firefighters (a job dominated by men). That is not real. Women on average earn approximately 77% of what men earn in identical positions. Women CFOs earn only 84% of what men CFOs make, at companies with the same market values (so “women are only CFOs of corporations that don’t make any money” is not a valid protest). This is what feminists are protesting.
Also teachers should make more money because are you kidding me? Doing their best to keep the country literate and math-capable? That is a societally valuable job. That is more valuable to us all than pro-business lobbying firms.
3. Women are smarter because they don’t hump everything they can. You know what perpetuates rape culture? Saying men can’t control their sexuality, but women can (because they don’t have any unless they are socially deviant), and therefore women must control all people’s sexuality. You know what feminists don’t like? Rape culture. Women are permitted only to be sexual in ways that are sexy to men, if you were thinking “BUT COSMO SAYS…”. Even Cosmo’s rare article about women masturbating includes “do it in front of your guy he’ll think it’s so hot!” Deviance is someone who is not a man enjoying sex for themselves, and not for someone else. Feminists also don’t like that (although I guess Jezebel would protest that).
4. Women are more spiritually evolved than men. I have read exactly one book that dealt with this in an incredibly patronizing, misogynist way, and not being a spiritual person or a person that spends time with people who talk about spirituality, I do not think I can adequately address this beyond feminists aren’t all about putting women on a pedestal.
ETA: My friend Jyoti said, about this: “I was under the impression that the whole ‘women are more spiritual’ thing was a way of trying to make them accept their subservient roles in society with a promise of a better reward in the afterlife (at least in Christian societies),” which I think is a good evaluation. Needless to say, feminists are anti-“women unquestioningly accepting subservient roles because of their gender.”
5. You can’t say that because it’s offensive to women. You can say things that offend women, you’re just going to get called out on statements that espouse sexism. Individual women get offended by more than attacks on their gender. “Your argument is bad” would probably offend a lot of women to hear, but that isn’t the same as “women are bad at science,” which is misogynist.