Earlier quoted context omitted.
People's qualifications are not all the same. Imagine that Google wants to hire 1,000 people, but 10,000 people apply for a job. Then Google logically ought to take the best 1,000 people that apply. With diversity quota's, the company may decide to hire a less able woman in favor of a more able man.
The company may also decide to hire a less able man in favor of a more able woman. Given that the vast majority of incompetent people I've worked with have been men (if not all of them), I'm surprised to see less attention to this phrasing of the problem. Maybe it is too politically incorrect to bring up?
That the vast majority of incompetent people you've worked with have been men can be explained by the gender ratio at Google. If most workers are men, then most incompetent workers would also be men, if men and women are equally likely to be incompetent.
My impression is that female workers at Google disproportionately work in the less technically hardcore jobs, which may actually be easier to be competent at or you may interact with those workers differently. So this may also skew your anecdotal observation.
Damore may have been worried about an increase in pressure to hire women leading to hiring women for the more technically hardcore jobs, which given the few female applicants for these jobs, could then lead or may already have led to worse hires then if there had been no pressure by the company to have pro-female gender bias.