I think he's being fired more for the severe PR fallout that resulted in the way he tried to start the conversation, than for the content of the manifesto.
I'd go one step further and say that he's being fired for completely misunderstanding the nature of Google's diversity efforts. He's responding to an attempt to create an equitable work environment. Google is more interested in creating a PR narrative.
These are complex issues that will take decades to fix starting with programs at the elementary school level and fundamental shifts in the messaging and feedback our society gives to children, young adults and all the way up to college students. And yet people are expecting Google to make significant progress on the issue within a couple of years. It's not really a realistic expectation to have of Google, but there are real market consequences for Google if they're seen not to care enough.
Google can make it look like they truly care about it and are solving it, but only if people don't look too closely or start pointing out flaws. This manifesto is an exercise in looking too closely and pointing out flaws. Whether his points, themselves, are flawed or whether they have merit is entirely beside the point.
> "we should expect to see people with certain characteristics in tech, in the same way we see people with certain characteristics in race-car driving. that's no reason to discriminate positively or negatively against race car driver candidates."
I think he did make a point similar to that. Unfortunately he stirred the hornets nest (most, I think) by pointing to the gender-wage relationship.
And you just (mostly) summarized it with a single sentence. The fact that such a screed was written at all is a problem. These kinds of arguments require very precise language in order to minimize misunderstandings and deflections.