This is very true and likely part of the equation, but the other part is that despite overwhelming evidence that companies with women in leadership do better and make more money, a lot of men (and some women) have a hard time envisioning women as as smart, as competent, and as worthy of leadership as men. A certain amount of that stems from patriarchal notions about women being opposite of and complimentary to men. Women in power still have to deal with the "authority gap" and walking the fine line between being seen as tough enough to viewed as competent, but also likable enough to be seen as not a ball-buster and a bitch.
When journalist Mary Ann Sieghart set out to document the ways that women are held back by a cultural presumption of their inferiority, she found reams of data to support her case — and heard stories of how it affects even the most successful women in the world. The authority gap: why women still aren’t taken seriously