Of course it is impossible, but in order to hypothetically examine the underlying parts you have to remove certain parts/simplify the "equation".
And of course they are "coded" since they have milk, only they can bear a child. Infants can't care for themselves, the human mother must have an instinct (code?) to care/feed the baby, otherwise the baby dies. In the first I don't know how many months the baby cannot even walk, since the head is much larger/heavier than any other body parts and the muscular structure is weak. If women are not coded for this behaviour we would've died out long time ago. Can we agree on this?
Of course the terms like coded might have totally different meaning for the expert, I only have a general understanding of this topic. You seem to be well versed, as far as I can deduce. So it's up to you whether to interpret them literally.
Okay, okay. So then, what's you take on this debate? Why are there more male directors, entrepreneurs, CEOs? Is this normal? Does this needs to be fixed? Is this the result of the male centric conditioning of our society? And if so what's the good way to approach and/or eliminate it?
Well these "information" are not coded as literally or functionally as you describe, but in a much more primordial and mechanic way. For example when baby sea turtles are born, nothing in their genetic tells them they have to rush to the ocean not to get eaten by seagulls, rather is encoded that when their nostrils detect ionised water particule in the air they roughly follow it to join their habitat, but we don't know if the notion of danger and therefor rushing is encoded and if they can hear and want to join their parent calling in the direction of the sea.
The same way, caring for offspring is encoded both in males and females at a very root level, but the way even the instinct is enacted or configuring is highly dependant on emergent first (since we were "born" out of nature), environmental, then social and finally societal, in ways that highly varies, again depending on culture and civilisation. In some africans tribes for example, it is consider that the mother bearing the child (which is a determined function unlike the attitude) is too vulnerable or fragilised by birthing to care for the baby, which males are therefor in charge of, until comes the time for "education".
In some ancient societies, in fact pretty much like lions, men having a bigger mass and taler size (although a lower muscle to fat ratio than women), where in charge of keeping the territory, harvesting and educating the child while female who were higher in muscle ratio, but also shorter in size, and therefor had better agility and stealth, were in charge of hunting, charting and trading.
So my answer to the last question is still the three points above as to why there are more male "leaders", put simply men are conditioned to pursue external endeavors in order to valuate themselves and actively mate, while women are conditioned to pursue "internal" as in social, familial, sexual endeavour in order to valuate themselves and passively attract.
BUT the problem is those norms are contradictory with the individualistic nature of human, and that's the problem of normative paradigm which always evolve, progress and sometimes regress when stalling: those norms are based on obsolete, sometimes centuries old observations then categorisation of humans, those categorisations transforming into conditioning, and those conditioning orienting individuals in lots of alienating, contradictory and frustrating ways, from which the individual responsibility is to emancipate and become the true unique individual they are. These true individual don't map on the norm, especially restrictive ones, one of them being gender (not be confused with sexes).
It's a lot more complex of course but all in all, in an ideal -meritocratic- and hierarchical society which we're far from, the best leaders amongst all population categories should be represented statistically in ways that proportionally match the population ie. there should be 50/50 men and women, but not by force or correction otherwise it's not meritocratic, neither should there not be 50/50 which is the sign of suboptimal discriminatory society, but by forces of individual emancipation on one hand (which is what feminism defended until it was corrupted by wokes into neo-feminism) and societies responsibilities (in fighting barriers, differential treatment, biased projections and conditioning or straight up discrimination). The difficulty nowadays is the first part, which in turns discredits or weakens the second, which in turn makes emancipation even harder or twisted, and so on. Overall, it's a hundreds time more complex, so much so that outside of the few occasional geniuses, the whole machine progresses very slowly and sometimes regresses or crashes.