I see two sides to this problem.
1) Getting him to stop expressing such things in public
This requires speedy action. Normally people have a resistance to change for others, but they are morelikely to change if there is a perceived benefit or they spot a drawback in their current behavior.
So I would:
- Tell him that it makes you feel uncomfortable. If he trully appreaciates you and doesn't think you are weaklying for beeing bothered by his comments it should at least make him think twice. Of course this enough won't work from what you have said.
- Tell him that if he continues it will hurt your and his public profile and ergo your career. Even if you were to agree, expressing such extreme views in public are likely to cause backlash unless you are in an environment where everyone thinks like that. This should get him to stop if he is smart, nowdays saying anything like what he is saying in a public setting can have greatly negative consequences. Also I think, given his views on the matter he should be prompt to agree since he thinks women are out to get men.
- Tell him that he sounds bitter, because he is spitting hate and not facts. Some people don't like to be seen like old bitter grinchs, and the way he is expressing, he just sounds like an old grunt. One thing is saying "In study X or Z 60% of women are found to do U or Y" and something entirely different is to be pulling comments with no basis but his own feelings.
To sum up, you need to tell him things that will make him stop for his own good, not for the "women".
2) Getting him to stop altogether
This may be near to impossible. It is really hard for people to change. And you may not want to take up this endeavour, but if you do, know it will be hard.
You need to engage him in a emotional level and make him see the problem from different angles, usually people have very fixed views over things but when you help them see the issue at hand from another angle it helps them change their mind and open their horizons.
Many great changes come from great trauma, and I feel this is going to be a great change. That is why you see so many people that for example were against dead penalty and then when someone close to them is killed by a criminal, all of the sudden want criminals to burn in stakes. So if you take this a general basis for change you can gather people change when something touches them internally, when something triggers a chord in their heart that they may not have even know it was there and it causes them to reevaluate their beliefs.
You need him to reevaluate his beliefs. But in order to do that, you have to know if this person is a good person. I asume you hang out with him, because he is a "normal" good person, he doesn't have some mental condition that will make him see things different and he doesn't take joy in hurting others. I clarify this because, how you approach thigns should depend on the mental disorder, if he's got one. So I am asuming he doesn't because you haven't said so. And I am asuming all in all, that he is a good person, what I mean, he doesn't take pleasure in other people's suffering, because I would guess you wouldn't want to be his friend otherwise.
Now we don't want to go and actually cause him trauma, so what is the next best thing? We need to try and reach and ring that chord, his innerself, through emotional engagement and empathy.
All of us are someone in the inside, that is not necesarily what it's seen in the outside, you can not hope for him to change in the outside if he doesn't change in the inside.
So first, start by showing empathy towards him and try to understand why is he saying these things. Did someone in the past wrongly accused him or someone he cared for? If that is the case, then you know why he is so bitter about this.
If that it is not the case, ask him directly what has he lost at the hand of women that he complains so much about the whole situation? Many people are actually quite influenced by the exposition these issues get in the media which makes them feel that false accusations are all the rage.
Counter his biases: If he was wrongly accused or if he is drawing his opinion out of the media. He is falling victim of several cognitive biases. For example, we can't take the cases highlighted in the media as statistical input. The media will showcase things that sell newspaper, because they seem interesting. Saying "Woman proven to falsely accuse CEO" sells more newspapers than "There are only 2% of false accusations". Now of course we get reports of both things, but where you may get One report talking about the statistics of false accusations, you will get many reports of different scenarios of false accusations. This leads people to believe there are way more false accusations than actually are. If he or someone close to him was falsely acused then all of his thoughts regarding this incident are heavily biased towards that experience.
So start by showing him that what you mostly see in the media doesn't reflect real statistics. Finding very accurate statistics on these topics is really hard because people don't report, and if you are not found guilty doesn't necesarily mean you are inocent, so it is a really hard topic. But I found this article in particular very interesting towards proving this point Men are more likely to be raped than be falsely accused of rape Now that is a showstopper and I think it will help him see that is not that common for men to be falsely accused and a lot of this feeling is coming from exposure in the media. Here are some more links on statistics on false accusations and how false accusations have rarely a lasting negative effect. In contraposition you can also show him the statistics of Sexual Assault and rape: The Criminal Justice System: Statistics, Sexual Assault in the United States, What We Know About Victims Of Sexual Assault In America.
Trigger empathy towards women: Now no matter what his life is, I think it is almost impossible to go around without having at least one good woman and good man in your life. Someone that you wouldn't like to suffer some misfortune. So try to drawn from that. Ask him how would he feel if this important women in his life were to hear him talk like that? It would be ideal if he had daughters because people tend to be very protective of their children and want the best for them. But if he doesn't he may have nieces or so. Ask him if he wants the best for them, if he doesn't want them to have all the oportunities in life? Wouldn't it be beautiful if every child in this world could dream of becoming anything they want and actually be able to do it? And not suffer because misguided people with bad information?
So start by making him think about those women he cares about (if they are younger it helps more, because we are usually protective towards the young), and what does he want for them. This will help to tear down his defenses. Humans are usually not that evil, we are just sometimes closed up to other people and turtled up in our own beliefs and world and we fail to notice those around us and their needs. But those defenses many times go down when we think and consider of the people we love.
Next, face him with the ugly truth. Show him rape and sexual assault statistics (the ones from above could help). And then show sexual assault consequences. You can search for rape survivors testimonies for example. I would avoid anything of anyone that has been on the media lately, because I feel his anger probably is directed towards some of them.
Then you can go all the way down through the rabit hole and talk to him about all the issues women face because of misogyny and these outdated world views.
I can tell you, it is hard to be a woman, and have to deal with men that don't know how to approach women in a non-sexual way. Or that think you are "emotional" and as consequences anything you say is tainted by emotion. Are all men like that? Of course not, but Toxic people tend to be more vocal than non-toxic. Non-toxic people many times tend to remain silent because they don't like to antagonize. That is why there are so many articles that talk about how we need men to be women allies. And that is also why I hate when articles talk about all men like they are trash, not all men are like that (btw there are many misogynistic women out there too). It can be exahusting to have your every thought second guessed, to deal with inappropiate hugs, etc. Most women I think, one way or another, have been mistreated and put down just for being women at one or more points of their lifes. Women just don't denounce all of this constantly. Also you can't denounce everyhting, as a lot of this situations are a lot of "he said, she said", which turn into "she just want attention or money that is why she is accusing".
Power corruption is not limited to steal money: sometimes I am surprised at how naive people can be. Everyone out there can understand and believe easily, if someone with power is accused of stealing money. I dare say people don't even have an issue to believe someone with power would murder. But you bring up that people with power harras and sexually assault too, and all of the sudden that is not possible.
Power corruption has a lot to do with doing things because you can. Of course many of those men accused of rape could get laid with a ton of women without need to rape anyone, but that is not the point. The point is not just having sex, is having sex with anyone you want, just because you can, whether they like it or not. The point is having more, of anything, more power, more money, more sex.
Make him explain his misognystic position: Ask him what does he mean when he says he is a misogynist. Sometimes when people say things outrageous like that, they falter when you ask them to explain them. Because they are just saying things for the "impact".
Once he explained his "mysogeny" ask him, What is going to happen if he ever has a baby girl? Will he put her in chains and take her to his basement so she doesn't see the world and doesn't want things that every men can get and no one questions his right to it? How will he explain his bias to that baby girl?
Ask him if he is in favor of slavery? Because expecting women to come to this world to only bear and take care of children regardless of what they want, is basically slavery. And not only that, is unfair to men, there are many men that would love the opportunity to be more involved in raising their children, but if it were only a "female" job those men wouldn't be able to do it. Children favor from having everyone in the family involved in their education.
Ask him, literally, if you were born to this world a woman and you wanted to be an engineer, and you were driven and smart, and have great ideas, would it be fair to be told you have to stay home just because you are a woman?
Point out that much is to be gained from diversity: The more point of views you can have over a subject the more you can understand it, that is why diversity is important.
There is also the other side of statistics, the positive, for example: WOMEN ON BOARDS Diversity in general is good for business.
Men sue too: he said that hiring a woman is buying yourself a sexual harrasment sue. But the reality is that men and women can sue for a variety of reasons, and sexual harrasment is not the top cause of sues and there are other kind of harassment too.
Finally Women and Men need to be allies, not enemies, and good-natured women and men will never have an issue with each other, good-natured men don't use their power to get sexual favors from women, and good-natured women don't falsely accuse men. But as long as we stand as enemies the problems will increase.
If nothing of all of these works, well I advise you to step away from him gradually, he will hurt your career and make you bitter. It is hard to deal with people that has such extreme views and don't want to listen to other people's point of view.
In the past I have to deal with people that have this kind of views, some where close to me, some where people I barely knew. It is interesting to see how sometimes they were raised by oppresive parents that lead them to believe theirs also opprosive points of view. Many people as I said think what you see most in the media is what is happening, when it is not the case, so showing actual statistics helps them have an "eureka" moment about reality.
Usually people, as I said, are good, and when you make them see how their view is hurting others, they stop. But sometimes people don't want to see, and in that case you need to think of yourself. If people keeps drawing away from him, maybe he will realiaze that he is doing something wrong and eventually will change. He has to see his actions have consequences too.