The other side of the same coin is whenever you receive nasty and undeserved feedback, you don't reply or argue.. You say "thank you for the feedback" and ruminate what good you can take out of that, if any. You don't fight back - not if you actually want to receive feedback in the future.
It's exactly what the article is saying: men are clamming up. If one doesn't know how to deliver excellent feedback/is worried about the packaging, the sane strategy is to just shut up. There's seldom a personal upside for delivering constructive feedback to anybody - and in a situation where bad delivery has unlimited downside, it's smart to just refrain from it.
I don't think it applies as much to coding practices, where you can provide specific and constructive advice and there's a concrete thing that can be debated (i.e., the changes to the code-base). What makes good business reasoning relies upon intangibles, like experience. But even here, one could point to examples of a strategy being used in the past and failing. You can't argue with the historical facts as being innately sexist. You could argue that the variables have changed, but then there's something concrete to talk about.
Edit: minor clarification