Privilege retreats. That’s the first thing to understand about it: it doesn’t just stand still, waiting for everyone else to catch up, but keeps moving. Sneak past the velvet rope keeping the great unwashed out of the party, and another rope will materialise behind it, guarding an even more exclusive gathering. Level a playing field, and soon the lucky few start getting invites to play in another more exclusive game. The good stuff always seems to be just out of reach.

And that’s as good a way as any of understanding not only this week’s hot mess of a debate about higher education but also why politics seems to have reversed itself into a cul-de-sac over social mobility more generally, clinging obstinately to ideas – bringing back grammar schools, scrapping tuition fees – that, while supposedly designed to help the poor, have a good chance of doing the opposite.

Whatever else is wrong with tuition fees, Jeremy Corbyn has been on shaky ground claiming that fewer working-class children now go to university because of them. A child from a disadvantaged background is more, not less, likely to go to college than in 2009, thanks to the vast expansion of university places. That may change if fees keep rising and students find themselves repaying punishing amounts of interest on their loans, but for some the velvet rope has clearly been lifted.

Many professions are becoming more stratified by class, not less, despite the rise in graduate numbers

But too many have ducked under it only to find that the real party is still elsewhere. Poorer students remain clustered in the least prestigious universities, often with the highest dropout rates, in courses that won’t guarantee a job. They’re paying the same £9,000 as kids reading law at Oxbridge, yet getting an experience that is light years apart and offers nothing like the same lifelong payback.

Meanwhile, many professions are becoming more stratified by class, not less, even as more children achieve a degree that should in theory have been their golden ticket. As old doors open, new ones seem to shut. Privilege continues to retreat. And according to a provocative new book from Richard Reeves, adviser to Nick Clegg during the coalition years, a highly convenient misunderstanding of what “privilege” actually means might have a lot to do with it.

Reeves’ book, Dream Hoarders, is ostensibly about why it’s no longer true that anyone can make it if they try in America, where he is now based. Much of it will, however, be uncomfortably familiar to Brits. He argues that blaming everything on a shadowy super-rich elite deviously rigging the system for themselves and their mates has become a tremendously helpful way of obscuring the truth, which is that the 99% are very much not all in the same sinking boat. A big swath of the upper-middle classes are ticking along very comfortably thanks, and doing their utmost to ensure their children will too.

The problem Reeves identifies lies not with the 1%, nor even the 7% who in Britain are privately educated, but with the professional and managerial classes more generally: those broadsheet-reading, often civic-minded and socially concerned 20% who might care passionately about inequality, but whose desire to do their best for their own children frequently (if sometimes accidentally) gets in the way. As one of Reeves’ thinktank colleagues confessed to him: “I spend my weekends decrying the problem of inequality, but then I spend my evenings and weekends adding to it.”

For even when they’re not knowingly giving their children an unfair leg-up – say, by wangling them a summer internship – Reeves argues that’s what professional parents effectively do, from long before those children are even born. Graduates mostly marry other graduates; and while smart parents aren’t guaranteed to produce smart children, it hardly hurts. They tend to delay having children until they’re emotionally and financially ready, and anxiously follow advice on everything from not smoking in pregnancy to reading bedtime stories.

And while it’s obviously not just middle-class families who do these things, wealthier parents can also afford reasonable maternity leave, good diets, good childcare, and nice, book-filled houses in the catchment areas of excellent state schools to which good teachers naturally gravitate. (As Clegg pointed out in a report for the Social Market Foundation this week, schools in poorer areas end up with more inexperienced teachers; seasoned staff tend to cluster in areas of existing excellence.)

Much of what the middle classes do isn’t even conscious – they’re just instinctively repeating what their parents did for them. And nor is it wrong, in itself. But it all gives their children a head start and, Reeves argues, helps explain how it’s possible to have a broadly meritocratic society where people are rewarded for their talents – where university is open to anyone who can get the right A-levels, say, and not just those with the right accent – and for it still not to be fair.

Some children simply get more chance than others to develop those talents, or get the top grades that are the passport to a Russell Group university. Even in a meritocracy, some families still hog the merit.

And the awkward truth about what Reeves calls “meritocracy without mobility” is that it actually suits the 20% pretty well, allowing them to feel good about the society they live in without much risking their own children’s prospects. They can cheerlead safely for opening up the party to everyone, confident in the knowledge that creating more opportunities for high-achieving children tends to work out pretty well for families like theirs.

All of which sheds light on the popularity of both expanding grammars (mainly colonised by middle-class children) and scrapping tuition fees (still predominantly paid by middle-class children). And while smart politicians understand the limitations of policies like this, it’s all too tempting to swim along with the electorally popular tide.

Would Labour have mobilised student voters so effectively if it had promised to cut fees only for mature students – whose numbers did fall sharply this year, perhaps because piling up debt is scarier when you’re older and may have other responsibilities in life – but not for 18-year-olds, still applying for uni at record levels?

None of these questions have easy answers. “Meritocracy isn’t everything” is an admittedly difficult sell on the doorstep. There are obviously limits on how far politicians can go in influencing parents’ relationships with their children, and privilege comes in too many guises ever to be eradicated entirely. But it may be a start if the middle classes were honest enough at least to recognise it in the mirror.