I agree that women understand better what it's like to be a woman, but this isn't really about that. It's about women and their perspective about men and the potential danger of men as violent rapists. The article linked by the OP suggested that "men would understand better" if they were kicked in the groin, but it also elaborated further by suggesting that it's also a matter of trying to size up situations. So, to carry through with the same analogy, a man would need to similarly size up who might kick them in the groin or not.
But in reality, men do have to size up other men in situations where there might be potential for confrontation or possibly violence. It may be an innate survival skill coupled with hard experience and a learned ability at situational awareness. Those of us who grew up in rough neighborhoods understand this and gain a certain street sense in the process. Men do understand violence and abuse, as men make up the majority of perpetrators and victims in that category. So, the notion that "men don't understand" just doesn't wash.
I'll freely admit there are some aspects that I can't understand from the women's point of view, since I'm not a woman. But I do understand that this is all in the context of the recent allegations made against Kavanaugh, along with other recent events, such as Bill Cosby's conviction and the flurry of allegations coming from the #metoo movement.
This is not about "excusing rape," but it's about attempting to chastise and call out men who fail to blindly and instantly believe every accusation that they come across. "You don't believe her! You're excusing rape!"
Rape is a crime. For that reason, it's a matter for law enforcement and the justice system to handle. I've never seen or witnessed a rape in my life. I've never been in a position to prevent or stop a rape, but if I ever find myself in such a position, I would do my best to stop the crime in progress within the boundaries of the law. I think it's unreasonable to expect men to become vigilantes or form lynch mobs, since that kind of thing has tainted our country's history for a long time. It's a matter for the law.
Of course, many women seem to think that it's as simple as "well, men should just stop raping and abusing women," and I agree with that. I also think there should be world peace, global socialism, and a universal brotherhood...er...siblinghood of humanity. But "what should be" and "what is" are always going to be different.
I think the law should punish rapists to its fullest extent, but I also believe there should be justice and fairness in the legal process so that innocent people aren't locked up for crimes they didn't commit.