> In engineering subjects, in Europe, men are the overwhelming majority in university.

In the US as well. But that doesn't tell us much about why. It's clear that it's not a first-order result of the behavior of companies; it could be a higher-order effect - for instance, students often choose a major based in part on the expected career to follow. If women expect to have a harder time in an industry that will impact their decisions, no matter how much we encourage them to like it.

So it might be "down to companies"; what you are presenting as evidence to the contrary isn't persuasive.

> After graduation they may choose jobs differently than men.

And they choose those jobs based, in part, on how they expect to be treated. Making sure they can expect to be treated fairly, can expect to find a job, and can expect good working conditions, is something that's within the purview of companies employing people in these roles.

> Then women are more likely to stop working when they have children,

This matches my understanding, but I don't think it makes up the bulk of the drop-off, much less the entirety. This is one part of why I suggested comparing attrition to other industries.

> or to choose a job with a schedule mores suited to looking after a family.

Schedules are within the control of a company. There are many engineering roles perfectly compatible with a light or flexible schedule. Meanwhile, nursing - the example you picked up-thread as stereotypically female - isn't known for either of those.

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I'm not saying that there's nothing to be done "upstream", in areas where individual companies have no influence. I am saying that present day companies do have things they can do to improve the situation; and that, insofar as we want to place blame, yesterday's and today's companies probably deserve some portion of it.