Women don't study math to become teachers: if they want to become teachers, they can study literature, language, history, chemistry, ... If they study math is because they like math.

I strongly suspect that the large majority starts in math with not specific plan.

Then, yes, they move away from academia. But it is an error to jump on the conclusion that it is because they wanted to do teaching and not because they saw how academia is for women in math and realized it's not worth the effort.

If indeed the fact that you can do teaching after math studies makes math a people-oriented job, then every studies are people-oriented, because you can always teach any field.

But that's not even the point. I'm not saying math is not people-oriented, I'm saying math is AS people-oriented AS computer science: if you want a people-oriented job, you can have one by doing math or by doing computer science, if you want a non-people-oriented job, you can have one by doing math or by doing computer science.

You are pretending that software developer is intrinsically not-people-oriented. This is incorrect: you need to work in team, both with other software engineers and other totally different teams, you need to build tools FOR other people, listen to them to know what they need and listen to them when they have complains or difficulties. The whole job is "how can I solve OTHER PEOPLE'S PROBLEMS by being the proxy between them and the computer machine instructions". How is that not people-oriented?

Again, there is this very very strange conception that software developer is somehow an extra-terrestrial activity. It feels like software developers have no idea of what other people do. Do you really think that an accountant that spend their whole career working for a specific internal department will meet and interact with more people than what a software developer can potentially? Or the people working in policy? Or the people working in operation and just managing the logistic? What about the cleaners? Is that a people-oriented job? I'm sure they create a lot of interesting relationship when they clean the office when everyone has left. What about a lab technician? What about a restaurant cook? Or an Amazon warehouse worker? (please, don't react to one of these examples, if you don't like one of them, feel free to just swap it to one of the thousand other examples where the employee will have less opportunity to interact with other humans than a software developer)

Sure, not every accountant job does not involve the same level of people interaction, and similarly, there are software development jobs where the dev can go away with not interacting much.

And sure, some developers, who are not people-oriented, find ways to make it work with them avoiding the people-aspect of their work. They usually need a manager to do this aspect of their job for them, and then complain that their manager is useless.

But again, it is not intrinsic to the work of software development. Software development is not a not-people-oriented job. Some people want it to be, they are somehow proud to be not-people-oriented (they are so not-people-oriented that it is very important for them to socially boast about how they are not-people-oriented), and they have big difficulties to admit that their job is not intrinsically not-people-oriented, and because of that, it is a fake image and a distorted reputation (with all the problem it causes: developers that keep moaning when they need to do people oriented tasks as if they are special and should not do it while it totally makes sense that it is part of their role).