And, it seems to me, based on my experience in the corporate world, that there is a lot of compartmentalization to automatically filter women as having "brains" that "do" certain kinds of work.   As an example:  Chief Administrative Officer = sure, women have the brains that can handle it;   Chief Technology Officer = not so much.    The compartmentalization pervades everything beyond mid-level management.

So, a woman can have smarts, but not the "right kind" of smarts for certain kinds of roles.   This is insidious and career development and training decisions reflect it.   This starts at lower levels, and ultimately becomes a self-fulfilling prophecy because the women don't have all the right training for senior roles in more technical areas before they reach the point of being serious contenders for senior roles.  It's never discussed as far as I know, it just happens.   It takes very strong leadership to overcome this hidden bias, and sometimes those leaders fall by the wayside.