Damore links to studies in his paper, but ignoring that for a second -- I could post a paper, and you could post a rebuttal, and blah blah blah -- but the point isn't that he's right or wrong, at least to me, the point is that if he intended to say that women, for whatever reason, simply disprefer professions like engineering, that it is a far less acerbic interpretation.
I'll freely offer that nothing in his paper affirms my interpretation of his view any more than yours, but if the only difference is that I'm more willing to assume good faith where you are not, then perhaps that's reason enough to not demand that he be insta-fired from any job he ever get, as many are asking to happen.