Although I'm not sure if what they're saying is true, it's entirely possible to be an aspect of patriarchal culture
and affect both men and women. For instance, feminists argue that "toxic masculinity" is harmful to both women
and men. Nevertheless, in my experience most people are averse to saying women have masculine traits; if a male is a strong leader, typically he's described as commanding, dominating, effective, strong-headed, whereas women in that position may be described as "bossy".
As such, if it is an aspect of patriarchal culture, it is more accurate to say that it is a patriarchal attitude that both men and women adopt, rather than it being something essentially "manly".