The problem isn't that there's differences between genders, but the assumption that 1) all people of a certain gender will think or act in accordance with the trends of their gender and 2) that the differences between genders means that one is better suited to certain tasks than the others.

For 1, while the behavior of men and women follows certain trends on a large scale, if you pick a random individual from each gender, they're likely to be as similar or different from each other as if you had selected two people of the same gender. So when you're doing something on an individual basis, like hiring for a position or electing someone to office, the average differences between the genders really doesn't matter and should not inform your decision more than the person's individual characteristics.

For 2, there's an assumption that there's exactly one type of person suited to a particular role, and that type of person is more likely to be of one particular gender. This assumption is false, though, as true innovation is not spurred by having a group of like-minded people, but by bringing a variety of viewpoints and personalities together so that problems can examined from every angle. Diversity in general ensures better coverage of an issue's potential pitfalls and a larger pool of knowledge and experience, so hiring from one gender because they're "naturally good at this kind of thing" is really only limiting the potential of the group.