There are lots of opinions that I might hold that would open my company up to lawsuits. In this case, he posted something that dramatically increases the likelyhood that some percentage of people fired will file suit, and this memo and the failure to reprimand/fire him will be part of the legal arsenal used against the company. Firing him is a simple mitigation strategy against this attack vector. ANY company that cares about lawsuits would have to make this move completely independently of the possible merits of his article. If it hadn't been leaked, he might not have needed to be fired. But once it was public news there was no sensible choice that Google could make. Again, I'm not trying to weigh in on his paper's content here, but as a simple legal precaution he needed to be fired.

Note that this isn't just about sexism, but lots of protected class opinions could fall into this category of 'express this openly and you'll be fired'. No company of any size would be able to tolerate it.