Reflecting on what Chuck was saying about the traditional gender roles; women had to be chaste, men brave. And the gendered insults: 'coward' and 'slut'.
And while there has been a movement to argue that 'sluthood' is honourable; oddly enough, there's no equivalent to argue that men don't have to be brave, that men don't have to be ready to lay their lives on the line for women - with no converse expectation.
It's still HeforShe, after all.
With regards to the Klingon sexual divisions, it's hard to tell what's deliberate and what's continuity errors. For example, "no women on the council" could have been a decision made after a progressive faction was defeated - and, knowing the Klingons, slaughtered.
Generally Trek is rather confusing about the place of women in it's Klingon society - maybe it's connected to the rise of the Warrior class, so that brute strength has even more importance over the course of the series - and presumably Klingons share human sexual dimorphism with regards to body strength.
Thus, the leaders will tend to be male on the grounds they can bash things gud!!! Not necessarily that they are good at leading.
And looking at how often Klingon civil wars seem to happen, poor leadership does seem to be their favoured style. They are good warriors - but that's it.
And that's just not enough.
I think in some future episodes they showed the Klingons joining the Federation? I can understand that. The Romulan empire seems to be a ruthless meritocracy, far more interested in cunning and treachery than physical might, and I would expect female rulers as often as male (and we did see a female Romulan captain in TOS, when no human female captain seemed possible).