How does pointing out difference in interest and a pretty well-established fact that women on average are more cooperative by any metrics prove that he should have claimed that women do not belong on google?
In fact, his point is that technology is not even for most men which he has made clear in other interviews.
The problem is the assumption that being cooperative is somehow a liability rather than a strength in a profession that's much more about cooperation than other engineering fields. (E.g. the trope that software is more complicated than an aircraft carrier because unlike in software, the toilet doesn't have modes of interaction with the steam launcher.)
Where does he claim it's a liability? As far as I remember I claim that this difference means that men and women generally make different choices. Can you point to where he says it's a liability?
His ultimate conclusion is that biological differences explain, at least by enough to reconsider diversity efforts, the difference in self selection into programming. Given that conclusion, your reading is even less charitable than mine. Under that reading, he’s literally just throwing out an unrelated difference between men and women, then asserting that’s why men disproportionately choose programming. Classic: premise -> ??? -> conclusion.
Reading his memo charitably, I think he’s assuming that cooperativeness contraindicates for programming preference, so at least he has a complete chain of reasoning, even if that assumption is wrong:
Women -> cooperative; cooperative -/-> programming; women -/-> programming.
In fact, his point is that technology is not even for most men which he has made clear in other interviews.