From her article we can conclude that Jenna Price wrote something sexist, but that is really all we can conclude without more information.
I do find it refreshing that nobody in this thread has yet argued that yes, it is appropriate to exclude men from consideration for this position.
I may be about to disappoint you, but bear with me.
In a society where gender discrimination was 50/50 in either direction, either gender could adequately fill this role. In a society where the balance is redressing with each passing year but the predominance of discrimination is still against women, I suspect only a woman has the lived experience to be effective and passionate in this area.
A man who has personal experience of gender discrimination (and it certainly does happen in the other direction, but it's not as entrenched) is likely to have a touch of the
Derecs about him, and there is a possibility he has sought the role for the wrong reasons. A woman with a comparable bias would at least be competent to identify discriminations which men, even the best of them, have a tendency to deny.
Having said that, I would be surprised by any claims that any of the women listed above would be subject to bias, if discharging this duty.
To put a man at the head of this particular Commission would be analogous to putting a lion in charge of the gazelle park. It may be a perfectly just and unbiassed lion but he would have to be something special, in terms of life experience, before he could come to an understanding of the dynamic that every woman lives with, the minute she enters the workforce.
There are historical and practical reasons, not to exclude men from consideration, but to only choose one if they show a level of understanding of the issues commensurate with that which comes with the territory of being female. There are so many eminently qualified gazelles out there.