I very much agree with the bulk of your post, most people are surprised to learn that woman on man domestic abuse is not at all uncommon. To quote wikipedia:
Straus and Gelles found in couples reporting spousal violence, 27% of the time the man struck the first blow; the woman in 24%. The rest of the time, the violence was mutual, with both partners brawling. The results were the same even when the most severe episodes of violence were analyzed. In order to counteract claims that the reporting data was skewed, female-only surveys were conducted, asking females to self-report, and the data was the same.
Gay and lesbian couples also have similar rates of domestic violence.
However, due to differences in strength women are much less likely to be seriously injured or killed by domestic abuse by men than vice versa. On the other hand, battered men are less likely to receive help from society for various obvious reasons. We really have to work against domestic violence in general, rather than just "violence against women".
Outside of the home, though, almost all violence committed against strangers is done by men, whereas almost all the violence that women commit is some form of domestic abuse.
However, again, I agree that women often suffer discrimination in the workplace and suffer disproportionately from sexual harassment.
However, due to differences in strength women are much less likely to be seriously injured or killed by domestic abuse by men than vice versa. On the other hand, battered men are less likely to receive help from society for various obvious reasons. We really have to work against domestic violence in general, rather than just "violence against women".
Outside of the home, though, almost all violence committed against strangers is done by men, whereas almost all the violence that women commit is some form of domestic abuse.
However, again, I agree that women often suffer discrimination in the workplace and suffer disproportionately from sexual harassment.