> "Teach men not to rape."
Many (most?) rapists are men. Many men are not rapists. These quotes aren't claiming that all men are rapists, and you've pulled them out of their social/political context in order to claim that they are. You're taking those quotes a bit out of context: they are responding to the cultural expectations/norms/memes of teaching women to avoid rape (and blaming them if they do not) instead of teaching men to not rape (and not really blaming them if they do). The studies (not feeling up for going and fetching them ATM, but let me know if you want me to) have generally shown that rape prevention teaching aimed at women reduces the chance that any particular woman will get raped, but does not reduce the overall incidence of male on female rape--while rape prevention teaching aimed at men does reduce the overall incidence of rape. (Note: female on male rape/sexual assault is generally thought to be much less common, but that may be due to serious stigmatization of reporting by men and poor metrics for measuring it--which is a separate issue than what is trying to be addressed by these sorts of slogans/philosophies. TBH, I think the best option may be universal "don't rape each other" training given to everyone, rather than classes aimed at preventing yourself from getting raped or preventing only men from raping.)
> Framing masculinity as a negative is anti-male. "Patriarchy" as a concept, regarding men as responsible for all the ills of the world, is also anti-male.
Patriarchy, as a sociological concept, is not about blaming men for the ills of the world. It refers to a hegemonic system which shoehorns both men and women into specific roles, values the male roles more, and punishes both men and women for stepping outside of them. It can (and is) bad for men as well as women--look up the research on what emotions are acceptable for men to show, how many preventable deaths occur because men didn't go to a doctor when they should have, etc. It is also tied to the devaluation of certain activities men might want to take part in (homosexuality, acting 'feminine' in any way, wearing dresses, whatever) and the potential for assault if people who were identified as male at birth don't go along with it (look up murder rates for MTF women, for instance). Framing some parts of masculinity as 'toxic'--inability to express emotions other than anger without being socially sanctioned, masculinity being tied up in punishing those who deviate (attacking homosexuals, crossdressers, etc.) is perfectly reasonable, too, and not an attack on men or masculinity as a whole--just the parts of it that involve hurting people. I will agree, however, that some folks don't seem to understand the nuance of what was is a formal academic term and misuse it. ('patriarchy'; this observation also applies to many other terms with formal academic contexts which were adopted by people without the background.)
> You've basically repeated what I said, except you seem to think sexism a good thing as long as it targets someone you perceive as "advantaged".
This is a subtle point, but: acknowledging that you are, in some ways, given huge advantages by society as a whole doesn't require you to feel terrible because of it. This is something I think a lot of people miss: privilege isn't something you can do something about in the present, aside from acknowledging that it benefits you and that you may not experience the same struggles and hardships, or may not experience struggles/hardship in the same way as someone without those benefits. The difference is subtle, but pretty important. The things you can do to address that, though, are listening to the experiences of those who don't have the systematic benefits you do, call out when you may be getting what seems to be an unfair advantage, and when possible, using your advantages to benefit those who do not have them. (A super simplistic example of the last would have been, as a man, voting for women's suffrage when they did not have the right to vote. A more subtle and modern example might be speaking up if you notice that a female colleague's ideas are often restated by and then credited to men, as you're likely to be perceived as a neutral party in a case like that.)