"Patriarchy" isn't a gendered insult, it's a description of the perceived traits of a social and economic system. But, if you'd prefer, feel free to substitute

"Patriarchy" isn't a gendered insult, it's a description of the perceived traits of a social and economic system. But, if you'd prefer, feel free to substitute "Our social system and values" for the word. Regardless of the terminology, the idea that power is held disproportionately by one group in no way implies that every member of that group is purely benefitted by that imbalance. Even as many men reap the benefits of our system, many of us are also harmed by it, as you pointed out. The expectation that women will parent and men will earn money causes a lot of men to miss out on or feel undervalued in parenting roles.