This really is only a possible explanation and I have no data to back it up.
By the way, you cite some statistics in your question without sources. The question is obviously how rigorous has your data analysis been?
Anyway, your question was interesting and yes you wouldn't think it would work that way. Here are some possible reasons:
In the less economically developed countries you mention, China, Russia, India, Iran, there is much less of a service industry. Eg tourism, beauty, marketing, PR, those sort of higher economic activities are less common. Anecdotally, I remember talking to an Indian student in a placement and when asked what proportion of students study engineering he said about 90%!
So for woman (and men) work is more about the basic necessities for living, the basic stuff like engineering. think of the UK 100 years ago. Who studied fashion then.
In western Europe and the US, women yes have access to education but they also have more choice. And I am suggesting that they go with their instincts and study what interests them more. Of course, this is talking very generally. My daughter is studying chemical engineering. On her course 30% are female - which is actually quite high.
If men and women had limited choice, eg the big area which is going to help you make a successful career is engineering, then you will probably do engineering. But if you have a vast array of choice, then you get people making different choices.
Lets face it, in the UK, there are not enough MEN doing engineering.