I think a lot of men don't realize that for most women, the feeling of walking around alone in a normal place is equivalent to a man walking around in a very sketchy neighborhood. Almost any man can overpower a woman and, if he really wanted to, kill her with his bare hands. But if a man wants to attack another man, his chance of success is only as good if he has a weapon of some kind.
It is for this reason that I encourage women to carry weapons and train with them. Even if it's just pepper spray, it's better than nothing. And like a fire extinguisher or a tourniquet, it only has to come in handy once to be worth all the trouble of keeping it around.