Sarah, I agree with most of your core points.
Except, in my view, standing up for women's equality and female empowerment ISN'T "misandry," by definition. It's common sense social justice.
The men who called you names for daring to bring up the topic of violence against women, or to point out the epidemic of male violence, are clearly threatened by the notion of losing unearned privilege and power.
And those who squawk "Not all men!" are usually reading too much into many statements where "not all men" is already implied, even if not explicitly stated.
In my view, true misandry would be holding the belief system that, because sexual violence is clearly a disproportionately male-fueled epidemic, it somehow means that males as a group are inherently "weaker" or have less intrinsic worth/value. Well, the BELIEF itself is only prejudice. But once that belief becomes actionable or behavioral (in terms of proposing policies, or trying to engineer/orchestrate new social norms) by women (or even by men who've internalized misandrist self-loathing), that's when it becomes misandry/sexism.
Of course, when we look at the vast majority of women (and men) who bring up male-driven violence and the systemic inequities/inequalities against women -- they are NOT trying to push for policies or interpersonal worldviews that would subjugate/marginalize one sex or gender over all others. They want what most people SHOULD want: a world where there is power-sharing and replacing unearned privilege with individualized recognition.
I apologize for the lengthy response. I agree with what you are saying about the common misappropriation/allegations of "misandry" in situations where it isn't actually being practiced. But in some spots within the article, you seem to be defining misandry in a way that sells short the true work of gender equality advocates.