Well, it should not be easy to misunderstand an attack on patriarchy as an attack on all men. That misunderstanding makes no sense, unless a person has certain rhetorical goals...
Generally, your approach is smart, but topics like this have to stir up emotion. I believe it is completely impossible to have a meaningful discussion about such topics, which affect people's lives, without getting emotional. I guess only people who are completely unaffected by the problem at hand can have the luxury of objective distance...
Much of the time, I can say "that thing you just agreed with is the feminist position on patriarchy," and it's like a lightbulb goes off in their head. People get ideas about words and concepts because their early exposure to them was negative. Give them a more accurate concept, then reintroduce the term.
It's really no different from how people assume the fem- in feminism means it's all about putting women ahead of men. I avoid calling myself feminist for the same reason I don't generally use the word patriarchy. Avoiding confusing terms in early conversations is a simple matter of effective communication.
Generally, your approach is smart, but topics like this have to stir up emotion. I believe it is completely impossible to have a meaningful discussion about such topics, which affect people's lives, without getting emotional. I guess only people who are completely unaffected by the problem at hand can have the luxury of objective distance...