That is all undeniable. There is of course a very compelling argument that rape is a gendered crime.
Sadly, men in general do not want to know, and see women's description of historical oppression as well as the impact of rape on our consciousness as a personal attack. They are apparently able to avoid acknowledging that rape is a problem created and inflicted upon the world by something innate in masculine nature.
It is too easy for men to avoid thinking about the problem because it is one that affects only women. It is too easy for men to look at rape in war and congratulate themselves that they or their ancestors were on the side that didn't do that, or that that is something only uncivilised Africans or hate-filled Serbs or cruel Russians would do to women -- it's something other men do, and recounting of historical oppression with rape as a tool thereof makes them very defensive on an individual or tribal level.
As seen fairly recently in the US, it is an item of belief that the issue of pregnancy resulting from rape is a non-starter because women's bodies are able to stop conceiving if 'real rape' has occurred 
. There's mental gymnastics for you. And then there is the subset of men who do not have enough empathy to understand how much rape hurts women because deep down they hate women and do not see them as human. I am not sure rational argument would sway them at all.
It's fairly clear when women are being raped en masse by invading armies what is going on (even if that spectacle only reinforces the belief that that is only done by other men). In the here and now, in the pub carpark, at the party or out on the date, or at home in bed with your husband, the issue of consent is paramount, and too easy to sidestep thanks to a convenient mental trick of seeing women's speech as unreliable when it comes to indicating what they want or don't want, as if they speak some alien or non-human language. It is too easy to portray women as beings who communicate in extra linguistic ways, who 'ask for it' telepathically. More mental gymnastics of course. This can only happen and can only be got away with when individual men feel completely entitled to use women/see women as less than human/have got the message that their behaviour is acceptable. If something only happens to women or if it only affects women badly, then in the minds of some men, it is not all that significant. The idea that men can share the position of being preyed upon (primarily by other men but also by women) might make inroads into the tendency to see rape of women as something that happens to beings that are somehow alien.
Women themselves for a long time bought into the reasoning that if a woman had been raped there must have been contributing factors on her part. Many still hold this belief. Women for their part have been conditioned to accept that there is something about some women that makes rape inevitable or even deserved, certainly not something they have a right to complain about. Again, the spectacle of rape in war is different; however, it's easy to avoid the big picture of general male oppression and see it as the work of specific armies or ethnic or racial groups, somewhere else, and not something any individual man is capable of doing to any individual woman.
The net result of the patriarchal system (which imo includes capitalism and acceptability of rape) can be seen in the few men who are very well off financially and a majority who struggle. I think if socialism (and other alternatives to capitalism) managed to appeal to people who have been the losers in capitalism then it will also be possible to define rape in a way that makes men sit up and understand it could happen to them. Just as asserting that rape can happen within marriage served to raise consciousness of what constitutes rape among women (and some men) and steer many away from the idea that rape is done to scantily dressed young women of 'loose morals', consciousness raising among men that men can also be raped would go far towards erasing the notion that it is about anything other than consent of the victim (as a matter of legal definition) and entitlement on the part of the perpetrator.
I feel the MRA may well end up hoist by its own petard if the definition of rape is extended.