I agree Damore's sources were unconvincing, but I've searched for sources disputing one of his most controversial claims (that women are more "neurotic" - an unfortunately named Big Five personality trait - than men) and haven't found any.
The Big Five is getting outdated. It was a popular method in the 90's, but doesn't hold up today for biological factor analysis because its lexical nature opens it to social biases:
>And that is what the Big Five represents: a consistent model of how humans reflect individuality using language, no more. There were no considerations of findings in neuroanatomy, neurochemistry, experimental psychology, observations of behavior of people or animals in real situations – none of this was used at the research stage leading to the development of the Big Five. In this sense we can say that the Big Five does not represent the structure of temperament or the structure of biologically based traits, even though lexical perception reflects some elements of it.
The big five can still be used for self-reported correlational analysis, but Damore used it in an argument against social constructs, when the method itself can be heavily biased by the social constructs he's arguing against.
His statements were within the mainstream interpretations of modern clinical psychology and evolutionary biology. That doesn't make them certain facts by any means, but it's important that we not misrepresent things here.
