This is sort of true. I'll talk about the aspect that is true. What is true is that men are an order of magnitude stronger than women on average. What isn't true is the violence part. Women are actually more violent then men and the reasoning is simple.
It's because men are stronger will do more damage if they get violent so men have a tendency to hold back. I don't know if you dealt with women a lot socially, but when women get frustrated they're more likely to pound you or push you with their pathetic little fists. They often have much less ability to control themselves.
This is supported by statistics: https://www.independent.co.uk/news/uk/home-news/women-are-mo... which should be taken with a grain of salt as violence from women against men is highly highly under reported.
The caveat here is that when it comes to actual damage men do far more greater damage, meaning that when a man actually does decide to lash out at a woman the damage is far greater and the crime far more severe. Outside of specific studies the severe crimes are the only ones that are reported. However, make no mistake, within studies that account for this bias, the numbers show women are more likely to be violent. In fact even those "territorial" men you talk about actually literally hold back when there's a woman around. There is no equal treatment here.
>My own experiences with fighting have not given me a fear of men in general, but they have certainly contributed to a caution that I have around certain types of men - in particular, around men who have either an animalistic concern with territoriality and status, a socioeconomic desperation that makes them willing to rob outsiders, or both. I try to steer clear not only of men of this type but also of entire demographics and parts of the world in which they are common.
Have you had much encounters with women? Even in dating and going to the club practically every aspect of their lives is centered around safety and caution. They rarely go out alone. Always with another man friend or with other groups of women (three at least) and when in bars or clubs even women who are strangers are always watching each others backs.
This is despite the very true fact that Men are actually much more likely to be the target of violence from other drunk men then women are when going to bars or clubs. The fear women have is biological and inbuilt as valid defenses for the more savage hunter and gatherer era. It is currently an outmoded standard of behavior that is no longer as relevant in modern society. But biology is biology and we are slaves to our biology.
Additionally it could be that women have these defenses because the consequences are much more severe. While a man is more likely to suffer from a violent attack from other men and women then a woman herself would, if a woman should get unlucky enough to suffer from an attack the consequences are extreme. This would be an argument in favor of your point of view, but still in support of the fact that women behave this way because of biology not reasoning. The biology is just an "reasonable" evolutionary response to the environmental pressure.