Reading that Natalie Portman believes that a female director having a particular gaze is reductive of women's individuality and point of view just shows that even someone as educated as her lacks media literacy and that today's discourse about cinematic gaze is based on very misguided and wrong understandings of the concepts.
If we look at social media, specifically tiktok, we would be lead to believe that a male gaze is what a man likes to look at and the female gaze is the opposite of that, what a woman likes to look at. How did we end up in this place? If we are to talk on such subjects, it would be wise to read upon some seminal works which stand as the basis and starting point of such concepts. We have to go back to John Berger and Laura Mulvey. And after we do that, we can nuance the discussion because there is so much to add to those initial understandings.
The concept of the male gaze has its origins in psychoanalitical theory, particularly scopophilia and Lacan's mirror stage. The man is the bearer of the look and the woman is that which bears the look and in the process she is transformed into an object. Mulvey explained that. All the elements of a film, from director, to DOP to the producing company, are creating this male gaze. But the problem with Mulvey's theory is that she assumed that the audience is strictly heterosexual. How does the concept still stand when a gay man is looking at the objectified woman on screen? Perhaps his gaze is upon the male character? Does that character became an eroticized object or not? How about a lesbian gaze? Is the woman's gaze from the audience the same as the director's?
I don't expect this and more from audiences across platforms, but I just want to point out that there's nothing simplistic there.
As to the concept of female gaze, there is little research, as compared to the male gaze in cinema and media, in order to have a definitive and encompassing theory. What I would say is that it's not the opposite of the male gaze. A female gaze does not automatically objectify men in a heterosexual sense, nor does it translate as objectifying women from a queer perspective.
Yet, it doesn't mean there shouldn't be an apparatus that helps us navigate texts as audiences but also for those who are creating the film and media texts.
Chantal Akerman in Jeanne Dielman did the opposite of the male gaze through filming techniques. She didn't fragment a woman's body and showed it as lacking eroticism. That's a choice that expresses a very clear message. Is it the female gaze? No, it is one of them, but I don't believe it is but one unique female perspective as Portman likes to think and as Akerman said at the time (as a context, Akerman refused the feminist label when the film came out).
There's plenty of women's perspectives in cinemas, but it is time to do the research that would do it justice. It's a lot of work and it must be intersectional because it has to be better and up to date with current understandings of women's identities.