No, that's not even close to being true.
Our "collective" responsibility is to teach children right from wrong and to teach them wisdom.
Is abuse wrong? Absolutely, and men and women should both be taught not to be abusive. While abuse of women by men is more visible and is decried more often, the opposite also occurs. More typically, men abuse physically while women abuse verbally or emotionally. In either case, the abuse is wrong.
Tolerating abuse of one's self is also wrong, and while there are some legitimate excuses, they are far fewer than society sometimes leads us to believe. Simply giving up and saying that one's self-image is too weak to walk away from the abuse is not an excuse. Giving up in that way is wrong.
Often abusers seem to be the most desirable of partners. Women abusers are sometimes very beautiful. Men abusers are sometimes very handsome and charming. The abuser's allure is no excuse for someone to stay with an abuser.
When someone is chronically and deliberately abusive, the law should punish the abuser. At the same time, most of the "no tolerance" and similar "strict" laws are mostly invitations for manipulation. If we as a society spent more time instilling children with self-respect, we'd go much further to stopping abuse.
Bill
Women are more likely to TRY to abuse physically, but they are simply less effective on the average. Many, many, many studies have show that women are more likely to initiate violence by a wide margin - though because of ineffectiveness, it gets categorized as emotional abuse. That is certainly not to say that violence by women is never a serious threat to a man - it most certainly can be, especially if pursued long enough or with weapons, even without the unusual case where the woman is stronger than the man.