It seems to me that the author would generally be sympathetic to Damore's memo (but who knows for sure) based on the views espoused in this post, so I don't quite understand your point.
The point seems fairly clear to me. arkis22 is pointing out that this author is making unfavorable generalizations about men, and stating that these generalizations are probably partly due to biology. Here, it is that women assign greater value to close friendships. Later, she states that:
"My experience confirms that teenage and college-age girls care more than boys do about solving real human problem (as opposed to competitive, self-oriented gain), forming close bonds with peers, and earning colleagues’ respect. I will not comment on whether this is caused by society or by biology; likely, it’s both and many factors in between."
This isn't wildly slanderous, but I think we can agree that caring more about real human problems is more admirable that pursuing "self-oriented" gain (or maybe not, randians might say self-oriented gain is the highest moral pursuit there is. I'd disagree, and I suspect the author here would as well).
So, we have that men pursue self-oriented gain, and women pursue solution to real world human problems, and this is partly due to biological differences between men and women.
Personally, I'm really not offended or bothered by this. She has every right to make this claim, and overall, I though it was a good essay.
I also think that arkis22 is interpreting these comments somewhat uncharitably. I don't need someone to go through a million footnotes and provisos and stating repeatedly that these are just averages. I am nearly certain that this writer would agree that some men care deeply about real human problems and relationships, and some women care more about self-oriented gain. I certainly don't think it improves the conversation when people get bogged down because they have to protect themselves against every possible uncharitable interpretation of an argument (she didn't say that arkis22 cares less about his friendships).
But we do live in a world where people who make comparable (perhaps less dramatic) claims about women face pretty serious censure.
I see, their point is that this particular woman can talk about biological differences but Damore can't. (I misinterpreted the poster as saying that the author was contradicting herself by rebuking Damore, which she wasn't, but that's not what they meant.)
That is a valid point. But the issue should be taken with Google's leadership and the individuals who unjustly raked Damore over the coals (his post-termination behavior notwithstanding). A reductive "women can get away with saying this but men can't" complaint doesn't really help anyone. It has truth to it, but it also feels unnecessarily confrontational and simplistic to me.
The poster also dismissed her claims with a mere "I really don't believe any of those statements" and then backed it with what seems to be a random assumption that the studies are biased and must have been seeking this particular outcome from the start, without any supporting evidence. I think the more sensible position is that Damore's gender difference claims and the author's gender difference claims are both correct (at least with the scientific evidence currently known). The us vs. them attitude is irritating.
I actually don't think that it's about who can make the criticism, I think it's more about what the criticism can be. A woman really isn't any freer than a man to make a sweeping generalization that is unfavorable to women, especially if it's attributed partially in biology. Interestingly, you really are largely free to do this in reverse, as we see (admittedly in a fairly mild form) from this article. Though be careful here - what seems like a compliment can in fact be very condescending.
The nuance of male friendship and popularity is probably just as complicated as female friendship and popularity. Complicated in a sense that I doubt any questionnaire captures the real truth.