Now isn't that a dishonest attempt to conflate concepts that are no more than homonyms at this point. The patriarchal society where in the leader of the household is the father does exist of course. The patriarchy that exists in feminist theory is almost a conspiracy theory that gets blamed for any inconvenience. It is the feminist equivalent of complaining about the Jews.
This is another example of what I was talking about in the first point. Many people, including some feminists, do mistakenly interpret "the patriarchy" as referring to a systematic conspiracy to oppress women. Rather, it simply refers to the idea that the society is structured around men, and women are oppressed and marginalized as a consequence of that structure, even without men as a group consciously planning to do so.