She has made the choice that academia is not for her, yes, but that was not for any academic reason: if we have any interest in improving academia, we should look at those reasons and see if we can't be more supportive to human beings in academia.
That said I'm all for a better deal for PhD students. They have a terrible deal.
(Aside: I personally agree with the female professor's comment - it would have been better if factually sexist behaviour was pointed out directly to the source to give them the opportunity to recognise it. But, behaviour like this needs to be called out somehow.)
No I'm suggesting if you are going to publicly accuse someone of sexism you should have something to back that up. I'm suggesting as you note yourself that it's unfair to say nothing and then suddenly post accusations on the internet. I'm saying that if her adviser is an asshole he wouldn't be the first - but there is nothing in her post or her circumstances that really indicates this.
There is actually no comment about whether or not her adviser is an asshole: you are drawing that conclusion yourself, presumably from the behaviour described.
Just because someone isn't directly disrespectful to you to your face doesn't mean they don't have bias or aren't sexist. It is not incumbent on the people with no power in that kind of relationship to provide evidence to satisfy your disbelief.
What if I'm a hiring manager, and I had 50 applications, 25 Male, 25 female. What if all the female candidates were really bad, and I ended up hiring 10 men? Is that sexism?
People are really reaching. I have yet to see a direct case of male vs female sexism on HN. It's usually heavily extrapolated and begging for an implication.
The word "sexist" does not appear in the article. Not even once.
I am guessing it were examples such as, "My former adviser has never graduated a female PhD student", that made you think "sexist"?
Notice that the conclusion and the label are yours, not hers.