He taught, did research at Harvard, was an associate professor. I'd like to see a debate where other psychologists - not tv hosts - are arguing with him. You are attacking the person and not bringing counter arguments to the table. Why there are more men in leading positions? There are equal amounts of good actors and actresses, yet way less directors.
He did a 5 year associate professorship which does not equate neither doing research nor being a researcher, but that's irrelevant.
Jordan Peterson doesn't debate actual psychologists or biologists because he would lose given how obvious the answer to the questions you ask are and have been. Rather he's a demagogue who has rhetorical debates with journalists, debaters and sjw looneys.
Anyway, the answer to your question is that: the same way the reason there's less black or asian people in leadership position doesn't have to do with them being racially incapable nor unwilling, the reason why there are less women in leading position is
A. Anthropological and Historic Normativity: in some tribes (that act as a counter-exemple and therefor proof of society vs nature) people see the vagina has being "dominant" in that it is protected and enveloping while the penis is seen has being "inferior" in that it is an exposed weakness that can hardly be used without a women endeavour or authorisation. This is an exemple of how deep and different the very basic conception of even our body, can differ and change a whole culture's and it's subsequent conditioning from a civilisation to another. Apply that to gender.
B. Conditioning and Performativity: women are brought up being constantly bashed the mind with valuing their own self-worth as being centred on their sexual/reproductive asset and the passive, external pursue of high-value (in perception) mate that will fill the active role, unlike men who are conditioned with actively pursuing external achievements, assets and performativity in order to augment their perceived self-worth to be more attractive and successful with women. AND this is important to understand today: conditioning is not some ethereal cloud, it's actually so tangible as to influence not just the mind, but also the brain structure, the hormonal receptivity and even maybe the epigenetic.
C. Discrimination: since nothing physically or intellectually prevents women from being directors, the difference in conditioning are heavy and powerful enough that at first there might less female than male directors candidates, but eventually there are enough that there should be a statistically representative proportion (so about 50%) of them represented. The problem is that of course many who pursue it are treated differently, barred or straight-up discriminated by very various means.
You add those three factors (which you have to explore through the countless books, essays and more importantly studies that document it) and you have a very precise, complex and substantiated reason why there is less women directors than men. Jordan Peterson is only spewing easily debunkable bullshit that are only successful because like in last centuries 1910/20/30s, we are in a conjecture of crisis, crash and eventually war during which reactionary rethoricians that history won't remember are successful by catering to the lowest "intuitions" people wishes to ear, to explain their own shortviews and understanding.
However the exception is that if Peterson pursues the Nietzschean, existentialist, gnostic path is on he might maybe right something interesting but that's not a given during his current limitations.