Then surely you have a problem with the idea that women should be afraid of the outside world?

I grew up in a relatively conservative household. My Mom would freak out if my sister had to walk/bike home from school alone for whatever reason, to the point where she would petition 13 year old me to bike the 2.4 km to the school to essentially escort my sister home. This was in the suburbs, in nice sunny weather and it was about a 20-25 minute walk. Keep in mind, my sister is only a year and a half younger than I am. But my mother was absolutely terrified she'd be kidnapped and raped in broad daylight in an essentially crime-free suburb...

This is not a healthy mindset to have, or to teach your kids. Stranger danger is a problem, and it causes people to be very fearful in situations where they really shouldn't be. It's no different if a woman is unjustifiably afraid of men, than if someone is unjustifiably afraid of black people or unjustifiably afraid of gay people.

I believe that women are safe to walk the streets at night (or atleast, just the same as anyone else is. YMMV in low income neighbourhoods.) , I think that they are safe to assert themselves when a guy crosses a boundary. I think believing otherwise goes completely contrary to feminist ideals, believing that women need extra protection or male escort just to be safe is an outdated viewpoint.

Public spaces are safer than they have ever been in the history of humanity. Crime is correlated to poverty, and there's less poverty than there has ever been in first world countries. If women are fearful in public for whatever reason, then it is very much a personal problem and not a societal one. Being afraid of men is not healthy, just like how being afraid of black people or gay people isn't an acceptable mentality either. Upbringing does not excuse any of those, so why should it excuse unjustified fear of men?

Grown women are not children to be coddled by the rest of society.