Matrimony means the state of being married: marriage.
Patrimony means an estate or heritage from one’s father or ancestors.
Apparently, it’s important for women to get married. It’s important for men to own things they didn’t pay for.
Both words originated in Latin based on the words for “mother” and “father” respectively. I conclude that something asymmetrical has been going on in both English and Latin for a long time.
Sue Burke 
I never thought of this. Very apt observation! I’ve always been thinking about matriarchy and patriarchy, which are fairly balanced terms, but never about matrimony and patrimony.
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