Or, to bring up a very timely example: currently there are no legal barriers to coming out as transgender (in the U.S., anyway). I still think it's reasonable to say that people are not "free to choose" to transition, because in many cases they will be ostracized or (legally) discriminated against for it. This is similar to the status of homosexuality (though it is a less direct analogy since there were many more laws explicitly prohibiting homosexuality).
Wait – I thought back then (1950s/60s/maybe 70s), "programming" refered to something more akin to data input, i.e., someone designed a program, and the "programmer" entered that program into the computer's memory, using punch cards or whatever . Later, this activity and the designing of a program was merged and done by a single person, as it is known today.
If this is true, then the mystery is not why women's preferences changed since the 1970s, but why their preferences seem to be different from men's, back then and today.
 You can still find this terminology in the hardware world. For example, storing the bitstream into an FPGA's SRAM or flash cells is called "programming the FPGA", and the little box which is sometimes necessary to do this, is called a "programmer" – which is kind of funny if you think about it.
That's exactly right, "programming" was considered secretarial work, and guess what, pretty much all secretaries were women.
Male engagement in programming exploded with the advent of personal computers in the 80s, and female engagement chugged along at the same growth rate as before.
The "programming as secretarial work" happened in the 50s and 60s which predates this data, so I haven't found a canonical source for that.
It can also be the case that the whole thing is a dynamical system (for example driven by desire to work in a field which already has majority in the same gender), and it somewhat chaotically "oscillates" around the equilibrium. So there really is not an causal explanation as such.
The "woman in programming" example is much better. Woman in programming started declining basically the moment computer games entered the market, since computer games are marketed primarily to males (outside of mobile, but that influence is fairly new). If we just simplify the whole problem to this one influence, woman are not programmers because of the marketing of "children toys". Is that bad, something we have to change? Nobody is really prevented from choosing to do certain freetime activities, to get exerience and motivation. They are just notpushed towards it. Still it leads to an unequal outcome.
Secondly, nowadays, men and women both play games at roughly the same rate (with women playing a little more by some metrics), but that doesn't seem to have improved the chances of women entering the programming industry. What is the explanation for that (besides that it's "new", which isn't really the case anymore)? Like many people, I got into programming as a result of video games--but I find it hard to believe that that alone is responsible for the entirety of the observed difference in behavior.
Finally, what is your explanation for the huge increase in the proportion of women in biology?
It is true that the gender imbalance in gaming has mostly smoothed out, but until that happened the software industry already turned mostly male. And even if nobody intends to erect barriers, in a group that's heavily skewed towards one demographic everything starts to cater towards that demographic, pushing everyone else away. So unsettling the balance once for long enough may be enough to explain where we are today.
>Finally, what is your explanation for the huge increase in the proportion of women in biology?
I honestly have no idea.
I don't know why less girls choose computer science than do boys, but I don't think it can be so heavily linked to gaming. The gaming community is actually sometimes far harsher on girls than the comp sci community, yet girls continue to choose gaming. In the gaming community, a girl is either a "thot" or she beats out every male who plays against her. If you're neither of these things the community still believes you're one of them and will react to you/attack you accordingly, usually defaulting to calling you a "thot".
In comp sci, the barrier is more about socializing. It may be a stereotype but I have noticed that many males in comp sci are the less socially-gifted ones. It is often not possible for a female to join such a group of males because they are scared of her. Other than that, the comp sci world in academia is far less disgusting than the gaming world and far less hostile. It's about avoidance instead of outright attack.
It could just be that girls enjoy programming less than boys do. I'm not saying that's definitely the case, I'm saying it seems more likely than not.
Last week I got to meet my cousin’s daughter for the first time. It was a family dinner and after everyone had eaten she pulled out her barbie dolls to play with. Since I‘ve been on HN for a few years now and this is not the first time I came across this topic I asked my cousin: Why does your daughter play with barbies? Did she choose the barbie doll or where they given to her?
My cousin, confused at first (because remember people: Most people don‘t really care that much about this stuff), answered: I think she chose herself, or maybe grandma gave one to her first.
So this could be it: The little girl might be free to choose as far as her mom is concerned, but is she _actually_ free to choose because she got influenced by her grandma first? Who‘s to say?
I hated them. They were obnoxious, lacked creativity, and smelled weird. I was a very willful child and loud about it, so I obviously refused to use these gifts in any capacity, but I think my refusal to play with toys I didn't like holds true for most children. If your cousin's girl didn't like the Barbie, she probably wouldn't play with it.
The whole point of childhood is having an idea of "I" without having a strong idea of identity so that we have a solid reference point for learning about the world without experiencing the blind spots that ego identities often impose. Consequently, we demand what we want and refuse what we don't want without thought. We rarely make compromises and our needs and wants cannot really be reasoned away by others (because our needs and wants in childhood are more instinctual/subconscious/impulsive than they are logical and experience-based).
I think we are most free to choose in childhood. By adulthood we have developed functioning identities and feel obligated to stay consistent with our idea of self. Many people take portions of their identification from a society's expectation of them, which is when freedom of choice becomes heavily blurred.
I think what is important here is to give children different options. I personally got a lot of toys from my family that I didn't use that much as a kid, most notably sports equipment. Meccano and (later, as it was expensive) Lego on the other hand.. Not to mention computers, that was love on the first sight.
Of course radical feminists reject all this evidence en masse and pretend its all a social construct, which is absolute nonsense.
To add to your rhetorical question of the inability to trace the source of gender preferences, some research on non-human primates was done.
In 2002, a study of vervet monkeys in the UK found male/female preferences for boy/girl toys.
That behavior was independently replicated in 2008 with rhesus monkeys in the USA displaying the same gender preferences.
There were also other studies of human infants displaying gender preferences, and studies showing similar preferences across different cultures and countries.
Those results will probably not change minds on either side because -- the belief that it's mostly nature or belief that it's mostly nurture -- is too ingrained for any evidence to modify.
If one leans towards innate differences, the studies confirm the beliefs.
If one leans toward cultural influences, then the studies are rejected with "monkeys are not humans!" or "who's to say the lab monkeys didn't learn boy/girl toy preferences from the researchers?"
The meta question then becomes: is it even possible to construct a nature/nurture science experiment that can actually convince one side or the other?
(The answer seems to be "no" based on several hundred years of debate on "nature vs nurture" with no final resolution.)
 2002 paper: https://www.ehbonline.org/article/S1090-5138(02)00107-1/abst...
 2008 paper: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2583786/