Patriarchy is about the SYSTEM, so that a class of people (men) have greater power than another class of people (women). This could mean, for example, that only men have the right to vote, or to pass on property or to choose where to live or whatever. This doesn't mean that every INDIVIDUAL in this society benefits from the system. For example, a son may be thrust into a position of responsibility in his father's company and fail miserably, because he is actually more suited to being a cello-player or childcare worker or whatever.
Humans and culture are complicated! At the moment I am living in Egypt. When a woman has a baby, she goes to live with her mother for a few months. After that she is the only one who feeds, washes, cleans, soothes, educates, disciplines, answers, monitors, plays with that child. As anyone who has spent any time around children knows, children are exhausting and can be pretty irritating. So, given the choice, these men choose not to help out in raising their children. BUT when I talk to fathers in my own country, they are all so thankful that society has changed and they now have a chance to be part of their children's lives.
A third reason is that when women can't participate, EVERYone misses out on what those people have to offer - whether it be art, algorithms or good management.