langurmonkey: If men still outnumber women among politicians, judges, senior civil servants and top business leaders, it is because women have less ambition towards getting those positions in life. Nothing to do with sexism.
But ask yourself why "women have less ambition towards getting those positions in life". As often, you don't take in account the cultural norms and values upstream.
Think of what Pierre Bourdieu calls the 'habitus', which is what determines, in general, the tendency of 'social reproduction'. It is the fact that, in practice, beyond the common sense discourses on "equality of chances", "opportunities" and "democracy", people live in little slots of limited horizons. That is : as they grow up, people tend to classify positions and activities as stuff that "aren't for them" or that are "not realistic" or that would be "presomptuous" or "out of place", "not serious to consider"... They don't even try, they get discouraged, they learn to not think about it, because they don't associate it to their identity. Because of these associations or dissociations of identities (origin, activity) in common sense, a kid from a low social class will easily consider that being an airline pilot, a lawyer or a brain surgeon is not "a thing for him", but a thing that "happens to others". While a bourgeois kid will spontaneously feel that these options are open to him, and that it would be "normal" for him to become any of these - it's staying part of his world.
A lot of little practical elements reinforce that feeling. Like how people around treat your ambitions, whether they take them seriously, dismiss them as a cute dream or discourage them as delusions of grandeur. Or whether they encourage relevant interests or discourage them and orient you to others. These surrounding people can be friends, family, teachers...It starts as early as toys kids are given (dolls to girls, construction tools and cars to boys), sometimes with school activities. Sometimes it's very subtle, an effect of expectations and different reactions to some activities or successes ("oooh you're going be a great engineer" or "fine and can you come help wash the dishes now"). Accumulations of little hints, not even consciously given, channel self-identifications and actual efforts in specific directions. When it comes to gender, it is often strengthened by explicit beliefs in what "boys/girls are good at", or what they should care for, what is "feminine" and "gay" or "manly" and "dyke-ish" (or whatever). This is also what positive discrimination tends to compensate, because when you see only one category of persons (white, male) in a given prestigious field of activity, it prevents you to project yourself to this activity when you belong to another category ("ah that's not for people like me anyway") and it further preserves this homogeneity.
See, we're back to our subject. Privileged people have a broader horizon of possibilities, in how they perceive themselves, in what is opened to them and expected from their lives. But some others have these horizons narrowed, they'd have to fight against the stream, or contradict some expectations (sometimes even ideas of "natural order"), they face invisible, sometimes unconscious barriers, that are built up by cultural representations. These are the cultural representations that feminism (amongst others) try to break down, by making us aware of how arbitrary these barriers are, and how they silenty shape our trajectories and our projects. When aware of this, we can overcome the barriers that limitate us, we can prevent cobuilding these barriers to others (as we do even with seemingly innocent jokes which imply these role distributions and enforce their silent "obviousness"), and we can try to change institutions that tend to strengthen or formalise these barriers (schools, for instance, often tend to increase these social-class-based differences of self-perceptions, instead of democratising opportunities).
And of course, again, the issue is pretty invisible to people who are not hindered by it, and who therefore underestimate how it hinders others. But as I said, to assess it, you have to check further back, at what, in our culture, makes some things look more "natural" to whom. Why women are lead to behave more "sexy" than men (leading to ridiculous bikini armors in fantasy), why do they not aim at the same high-level jobs as men, etc... "They just do/don't" is not a sufficient answer - it's an effect, not a cause.