

The problem with that is you are then putting the burden on a member of that hated group to present themselves as a paragon and suffer all the vitriol and abuse that gets hurled at them until the hateful person hopefully snaps out of it.
Having been the sole woman in many male-dominated spaces, I gotta tell ya, it is a special kind of hell to try to be that positive example.
I think the pay issue is a big contributor. Women are more likely to accept lower paying jobs, particularly ones like caring professions or teaching, whereas men have a tendency towards higher paying jobs (in part due to the lack of support for pregnancy, parental leave, and childcare expenses).