With respect to your first point, that's why I said "typically". I never assumed that those roles were universal, only common.
And while women can be violent as well, most of the cases where I've seen it, it's still markedly different from men. Women are less capable of causing serious harm (i.e. a punch from a typical woman vs a punch from a typical man has drastically different consequences). As a result, violent women often show less control, as the actions of a violent 120 lb woman don't have quite the same effects as a 250 lb muscled man, so they are less likely to learn the lessons that most men/boys learn early on.
As a result, the violent women I've seen are often quicker to violence, whereas most men have a much slower burn because when we turn violent, the consequences are much more dire.
All that aside, I never intended to say that violent women don't exist. But the average woman doesn't understand that aspect of men.