It has something to do with the fact that far more women get raped and sexually assaulted by men than men are raped or assaulted by women. We fear predatory men.
This is a true statement, but it skews the context. I don't like seeing it in this kind of discussion.
1. It chooses one of the most extreme examples if a serious crime where the vast majority of victims are women. Contrast with: Men are significantly more likely to be the victims of violent crime than women.
Would a women choose a potentially dangerous place to approach a man? Of course not. No more than typical males choose to spend their free time acting aggressively in dangerous neighborhoods.
Both groups act rationally to avoid unnecessary risks.
2. Crime statistics and what they actually mean in terms of risk management are not simple to interpret.
It's easy to ignore this fundamental truth: many crimes, notably crimes of violence, are committed by a rather small percentage of people (those with malignant ASPD are vastly over-represented).
It's "one person 250 crimes" rather than "250 people, one crime each".
One effect is that measures by society to curb bad behavior often have no effect on the actual perpetrators, but make life more difficult for the majority in the center of the "bell curve". Done on too large a scale , with many laws enacted according to this principle, and the overall effect can be very negative for the majority, and catastrophic for people at the other end of the bell curve to (e.g.) the ASPDs.
Regarding approaching the opposite sex:
Just to be clear, I understand this as approaches with the clear intention of making a social connection.
I wouldn't count being asked where the dairy products are in a supermarket, regardless of whether some people might use that (see below for a little more detail).
I've been approached for the former purpose enough times to share my experience , but not enough to claim it's statistically meaningful.
What I've found is that women (all but perhaps two or three in my case) seem very unskilled at making that kind of conversation. The approaches are typically simplistic, with the apparent expectation of the man doing all the "social work" that's needed to move forward.
So in my experience, an M->F approach isn't really the same thing as an F->M approach. It's more like two different activities with the same name.