The word is easy to misunderstand. I usually just avoid it entirely and discuss the symptoms instead. Most people agree that what patriarchy is is something that needs changing, so it's silly to stick with a word that so reliably muddies what should be an uncontroversial conversation.
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.
