> where male privilege exceeds female privilege.
I'm not sure I can categorically agree with this. While male privilege exists over women, I find it ludicrous to suggest that white women are less privileged overall than black men, despite black men benefiting from male privilege. I think many of the misunderstandings that occur when discussing privilege come about due to using only a few easily categorized traits in defining privileges, rather than a broader set that also include things like socio-economic conditions, health, upbringing, and a variety of personality or physical traits.
I don't think it's that hard. There are unfair privileges to either gender, but the male ones are vastly larger.
This kind of claim (regardless of which direction you're making the claim in) ony makes sense if you reduce "privilege" into a single dimension. Which I don't think you can.
This doesn't necessarily follow, because insofar as male privilege exists, so does female privilege (such as no draft, "women and children first", the "women are wonderful " effect and the fact that women represent the majority of the voting base), so it's really hard to say one sex is more privileged than the other, rather than just privileged differently.