Colin's response nails it on the head (but also, some of the people Cathy is talking about are really, really scary smart).
For what it's worth, around 15 years ago, I personally had a "traumatic" and relevant experience involving the author (Cathy O'Neil) of the article we're discussing here, which I've never told anybody about. We are both number theorists, with a similar educational track (Berkeley, Harvard, etc., at similar times). She and I were hanging out in a pub in Cambridge, MA, and I was showing her a list of research projects I was very excited about and working on.
First, some background about me. In grad school at Berkeley, I had changed from worrying about "being a genius", to just being completely obsessed with doing mathematics research all the time, and actively simply not thinking about myself or social things. I had many clear experiences when working on research problems in which if I thought at all about myself and whether or not I was "smart" (or anything social), my progress would completely stop; however, if I could clear my mind of such worries -- about myself or others, then I could prove theorems and do good mathematics. So at the time I really embraced mathematics research itself over social concerns.
Anyway, Cathy and I were in a bar, and I was showing her (on my laptop), my list of projects. I really hoped she would find some of them interesting, and we might coauthor a paper together, since her thesis research was closely related to mine, but approached things from a completely different (more geometric) direction, which I personally found extremely difficult (at least, I didn't have the "interest" to master that approach, in the sense of Colin's comment). Well this is not at all what happened! Instead, of getting excited by any of the projects I proposed, Cathy got really, really angry at me for (I guess) intimidating her (?). I was never sure. I genuinely meant no harm.
For me personally at least, somehow worrying about the social aspects of research mathematics too much would make it impossible for me to actually do mathematics. I wonder if some of the other people Cathy alludes to in the article are similar, and if this has consequences. Anyway, it was a lesson to me at the time of the extent to which having a sense of "being in the zone" and not thinking about oneself (or social and emotional issues at all), can simultaneously be very conducive to research mathematics and also really piss off certain people.
I make no claims to be a genius or "emotionally mature" at the time, and I'm a different person today than I was then. However, there is (at least for me) a real psychological conflict between the social aspects of thinking about research and actually doing research; it is a very difficult challenge to balance the two.