Patriarchy is a social system that we all participate in to some extent, but it has historically and still is today something that benefits men more than women (although it harms men as well). If men want to consider themselves strong, they need to be strong enough to grapple with that and the ways they uphold it - either consciously or subconscious, either intentionally, or with their silence and inaction.

Matriarchy would be a dominance hierarchy system with women having much more power and social influence. I don't think such a thing has ever existed - maybe the Minoans, but matrillineal cultures favor balance between men and women, not "power over" situations, so probably not.