While hiking alone can have serious drawbacks, and while being raped can be more of an issue for a woman, a just-plain-psycho can be a danger to anyone, male or female.
If there are at least two people hiking together, one can break his/her leg, and the other can pound his/her head in with a rock.
Assuming that neither is armed with anything more than a knife.
But leaving rapists and other psychos out of a hiking picture (they're relatively rare, after all), it's simply a fact of life that hiking alone is more dangerous than hiking with at least one other person. If it's a danger that you can live with comfortably, fine. It's an individual decision.
I have hiked alone with just a dog, and had no problems. Most of my dogs have been shepherd types with dark faces (everyone 'knows' black-faced dogs are mean!). I really do focus on a guy whose first question is, "Does the dog bite?" ("Only when someone bothers me.")
There are actually many advantages to hiking with a dog: they're willing to go wherever you want to go, they don't talk all the time, they're in no particular hurry, and eating anytime is always a good idea.
Sue