I am "she" in the OP who doesn't believe in the patriarchy 
I do think it is a bit like religion. Religious people see evidence of god everywhere. Sometimes I get into discussion with someone about their faith and they say "god is not really a super human-like figure ('man with a beard') who answers prayers, it is more like all that is good in the world". Well I believe in "all that is good in the world" I just don't call it god, or ascribe it to a single cause.
The answers here that the patriarchy is all that is bad in society (or at least in relation to men and women) remind me of that conversation.
We could just ignore the differences and each understand patriarchy in our own way. But I think it undermines clear thinking about issues by giving pat answers.
When people say "the patriarchy loves/hates it when..." to support an argument which really means "I think it it is a bad/good idea to do this" it seems analogous to me to saying "god wants you to/doesn't want you to". Maybe it is just a short hand between people who agree with each other but I think it is sloppy - it stops people thinking through or spelling out why they think something is bad or good and arguing the point - because who wants to argue for the patriarchy?!?
There is a natural tendency in humans to want to explain things in terms of agency -goodies and badies, friends and foe. It is much more intuitively attractive to say that god created the world for a purpose than to say that it evolved through billions of purposeless interactions. Similarly it feels more "true" to think that inequality between
men and women is because men have chosen to oppress women, and women have been duped and overpowered, than to try to understand the processes of biology and economics which underpin culture.
Ultimately I don't think "patriarchy" is useful as a way of understanding and explaining the state of the world. It separates biology and society and treats them as two different things. That human males and females are relatively different (not as different as some species, not as similar as others) indicates that there has always been a division of roles between males and females that goes beyond pregnancy and BF (which relate to all mammals) and that there was some evolutionary advantage for men to grow relatively muscley and aggressive, and women to develop concealed ovulation (both expensive strategies in evolutionary terms, so they must have been advantageous -because "men were stronger and wanted to control women's fertility" doesn't explain things - it begs an explanation)
The biggest reason I don't believe in patriarchy is that it falls for the naturalistic fallacy that natural means "good" (and that naturalistic explanations are justifications). This is just not true.
The patriarchy explanation seems to me very like the myth of "The Fall" (except this time Eve is duped). The idea that there was a time when there were humans very like us in character, ability and physiology but without the bad stuff is a myth. If you build feminism on that myth it intellectually shaky, even if it's moral impulses are mainly good.