Of course they do. And while there is overlap in the methods of signalling and enforcing dominance within the respective hierarchies the balance of competitive behaviours tends to be somewhat different.
In terms of this specific behaviour the penalty for not displaying sufficiently low initiative is less for a low status female than for a low status male while the rewards at the other end of the spectrum are also greater for the male showing leadership than the female doing the same. In respect to this particular trait and all else being equal this would lead to the expectation that there would be greater variance in male initiative taking behaviours than in females.
There are other forms of competition and signalling behaviour where the balance of importance leans more towards female hierarchies while the applicability to male competition is somewhat reduced.
The thing is, I have problems with acrasia which don't seem all that different from the men who describe it here.
For quite some time (with a partial reversal in the past century), passivity was taught as a quintessential female trait, which I'd say is confirmed by your use of "pussy" as meaning unduly subordinate-- for a male.
During a discussion today about the bizarre "can't get crap done" phenomenon that afflicts large fractions of our community, the suggestion came up that most people can't do anything where there is a perceived choice that includes the null option / "do nothing" as an option. Of which Michael Vassar made the following observation:
And if you're not the leader, it is not good for your reproductive fitness to act like one. In modern times the penalties for standing up are much lower, but our instincts haven't updated.
Interesting to reconsider the events of "To lead, you must stand up" in this light. It makes more sense if you read it as "None of those people had instincts saying it was a good idea to declare themselves the leader of the monkey tribe, in order to solve this particular coordination problem where 'do nothing' felt like a viable option" instead of "nobody had the initiative".