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> Why do women report higher levels of anxiety at Google, according to the manifesto? Because of their gender’s higher levels of “neuroticism.”

Neuroticism is one of the Big Five personality traits and, as such, is a very mainstream topic in the psychology of personality. Scare quotes are used to suggest that a word is being used inaccurately, or in an unusual way. As such, a reader of this article who is not familiar with the Big Five model (aka OCEAN/CANOE) is likely to erroneously believe that the memo author is using 'neuroticism' to mean to having a neurosis or some kind of mental illness, which would indeed be inaccurate here.