I've shared this before but I'll say it again as I think it's relevant here, though last time the jury was very divided as to whether my analogy held true.
I see gender inequality, of which rape is a product, as not actually being borne of gender itself, ie, men aren't genetically disposed towards being sexists pricks. It's a product of being human. Men are taught to be that way, and it has nothing to do with them being born with a penis, just the society in which they were born. And they happen to be the ones being born into the position of privilege.
I grew up as a white child in apartheid South Africa. We were raised in a racist society. We were actively taught, by media, society, our families, to be racist, to see black people as "lesser" and to expect them to service our needs. Not sexually, of course, but in various other demeaning ways like being house-maids working 12 hour days, 7 days a week for a pittance, and not being allowed to use the crockery in the house because they were "dirty". It was awful, it was appalling, but it was also just normal life. To us and to them.
Only once things changed, when revolution came and we had to change, when I travelled and saw how things were in the rest of the world, did we realise how utterly appalling things had been. I was the one in the position of privilege at that time, as men are now. I abused it, as men do now, because I was never taught differently. I'm deeply ashamed now, but that's how it was.
White South Africans weren't terrible people. They were otherwise lovely folk who would give you the clothes off their backs. As long as you were white. They were just a product of the deeply flawed society in which they lived. Now it's unimaginable that we lived that way. How could we not have seen how wrong it was? And I hope one day we'll look back on our current sexist society the same way, with deep horror and revulsion that we once accepted such blatant, obvious and damaging sexism as normal.
Men rape because our society teaches that women are "lesser". There to serve men sexually and be subservient domestically, to quietly tolerate abuse and just be grateful that they get anything at all.
It's not because they're men. It's because they're human and as a group, humans do terrible things to those they perceive as "lesser".