First, you have biological differences between men and women. These are reasonably well characterized, and the sorts of psychological differences that might impact the workplace are small but present. It's still very difficult to get into specifics, however, as definitions/measuring is difficult (lots of room for error here) but the thesis of 'this may be relevant, and we should be able to discuss this' is supported.
Then you have the various stereotypes about men and women that we observe in the current population. There's a lot of nuance here and, again, a lot of room to confirm your own biases, but on the whole there are certainly differences. The question is mostly nature vs. nurture and how much of this is cultural historical artifact.
The problem comes from trying to explain the latter with the former. This is difficult to do in a scientific way; the essay mentions castration and some cultural practices that can suggest some aspects of this relationship, but it's a far cry from being generally explanatory. It's all terribly specific and contextual and the state of the art is so far away from explaining bias/discrimination in hiring/employment that it's arguably not worth mentioning.
The equality/diversity contradiction is a good enough point to make, but it doesn't accomplish much. The real thesis is that Google's hiring practices are discriminatory, but there's not a clear scientific answer to that at all. Aiming for rough equality seems like a conservative approach; the distributions for these metrics suggest something like single-digit-percent differences between populations of men and women (i.e. lots of overlap due to variance). A 'worst-case' for discrimination against men seems very likely far less severe than the current state of discrimination against women where 9:1 ratios are not unheard of. And this is certainly a wonderful opportunity for debate and may not be correct, it currently is not proven to be incorrect by any stretch, and thus it cannot be claimed that the hiring practices are discriminatory.