I don’t think it’s about finding it personally offending but rather that it does paint all men in a certain light and I just don’t think that sort of generalizations are good.
I’d like to say that anyone who hears the reasoning “women have to be cautious around men because some men are capable of violence” and jumps immediately to “women think all men including me are violent and that’s wrong” is sorely missing the point.
I mean I think it went a bit further than that.
As someone interested in the discussion side of this issue and not the actual conflict, which you seem to understand, please tell me how you would handle someone strongly asserting to you that women are bigots because they avoid men or treat them differently when they don’t know how they’re going to react.
If you are acting differently towards someone because of their gender (or skin colour or religion), that would make them prejudiced at least. So I wouldn’t argue that point. I’d probably say they are prejudiced but that might be out of fear rather than malice and rather focus on what to do about that.