@AssassinatedBeauty You asked me what I wanted to say about “sexism, discrimination and equality” with regards to the letter. So I will now speculate as to why he wrote it and give you an answer.
I am not a scientist like @PricklyBall. However, I would hope that they would suggest we look to the simplest explanation first. The letter says it is written not against women but against the diversity programs so that would be the place to start.
I believe that there is evidence to back this up. Thanks to the structure of the legal and media systems there, when news breaks big in the US people come forward to bear witness to past behaviour. Sometimes genuine, often also false witnesses. No-one has said that this guy has a history of misogynist actions or speech only awkwardness suggesting this simple explanation works.
He quoted science and posts here have attacked it as being absent or wrong. From what I have read the science is there, it is correct and it is wrongly applied. In fact it could be so wrong as to be the case that where he says women are statistically “less likely”, that they could be “more likely”.
With the help of @MrGHardy we established that few understand the mathematics. The term “fewer” morphed into “less”. This even seemed to strike people like Yonatan Zunger, who, you would hope, could do better. His output has been picked up by journalists like the great Owen Jones (www.theguardian.com/commentisfree/2017/aug/08/google-sexist-memo-alt-right-martyr-james-damore). This misrepresentation grew hysterically. An ultimate illustration being from CNN “I don’t really like women anywhere near a computer” ( ).
If, as I speculate here, the author found themselves disconnected from the diversity programs then it is a serious issue for Google. The programs need engagement. The question is whether his attitude is unique? They need to ask his ex-colleagues. The challenge now is that in sacking him they have sent a message saying “we don’t want to hear the negatives”. They could have communicated a counter message “we did not take this action because the author criticised the programs” but didn't. I think the analysis in this article by Rachel Bitte is very good - fortune.com/2017/08/09/google-diversity-memo-uber-crisis/.
An individual does not have a PR machine to ensure they say all the right things and in the right way. My speculation is that he wanted to complain about the programs, not his colleagues, and the fact that he did it badly reflects that he is human, not that he is a monster.
To finally address your question then, and in no way do I mean to preach here this is just my view, I believe that equality stems from treating everyone as individuals with respect. I believe it involves working hard to not assume what they will think or how they will act and questioning, not projecting, one’s own preconceptions. To judge them by their performance and not by your perception. For me it is something you work at your whole life. In this context then I have found this text to have created great irony in those who reacted to it, reflecting perhaps that there is little genuine desire for equality anywhere.