

This is often driven by media portrayal. If young women aren’t seeing women being portrayed as directors in media, they might not make the mental leap to “I want to be a director, and I think it’s possible”. For example, the x files led to women in stem having more confidence in their choice of career (STEM career). https://geenadavisinstitute.org/research/the-scully-effect-i-want-to-believe-in-stem/
This has very little to do with my opinion of women’s agency and has more to do with my opinion on human agency in general. I have known many women in my stem field who are better than me at my job, and I know many that have faced discrimination/hostile work places.
I mention the Scully effect (see also the uhura effect) because as humans, we aren’t immune from propaganda, and when media companies accidentally or purposefully make a character that inspired people, it seems weird to not acknowledge it?
The number of big Hollywood directors is small, so general workplace trends might not be as noticable, but I still think that the typical director in media is depicted as male. I think that would have a noticable effect if you could find two populations who had experienced different depictions in media, and polled them about dream jobs.