Unfortunately, there are lots of examples in comments from women mocking, disparaging, or dismissing men's struggles just like there are comments from men mocking and disparaging women's struggles. Lots more where either men or women are not treating people as people but rather as synonymous with the label of their gender.
It's not really useful to compare the numbers (my vague sense is that men dismiss women's struggles more and women depersonalize men as "men" more, but it doesn't matter) , because our brains don't really work that way. The rate of each is high enough to make everyone feel attacked and invisible, and retreat into communities where the incidence of such attacks is rare.
I think you're right on target that the reactions Robert gets are often motivated by pride. However, if he were speaking this way to women it would be a really bad case of mansplaining, don't you think? Why would someone need to give up their pride in order to improve? Isn't improvement hard enough on its own without making people have to swallow their pride too?
I agree that men, in general, need to learn to be better at listening. But I think Robert's patronizing and sanctimonious tone is more likely to make men who are potentially open to listening decide it's better to stop instead. Doesn't it look, from the balance of the comments from men, like this is true? If you read Simon Fokt's fairly-similar-fundamentally except appealingly-presented advice and admonitions, you find that he doesn't get nearly so much pushback from men.
Consequently, I can't agree that this is fantastic. I think it's actually pretty bad. Just look how the last two sentences drip with scorn for the people he's supposedly trying to reach: "Can you do it? I believe in you!"