It has taken a surprisingly long time for the chickens to come home to roost. But watching Zarah Sultana, the 26-year-old new Labour MP for Coventry South, waving her student debt bill at ministers over the despatch box last week was a decisive moment in the henhouse all the same. How, she raged, was it fair that working-class kids such as her had ended up £50,000 in debt from going to college, while Boris Johnson sailed straight “from the playing fields of Eton to a free education at Oxford”?

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To accuse her of class warfare, as several Tories promptly did, is fundamentally missing the point. Age is the yawning divide between newcomers such as Sultana or Nottingham East’s Nadia Whittome – who dropped out of university halfway through because of money worries – and many of the ministers they’re facing across the floor of the Commons. While there’s nothing new in the argument that millennials got a raw deal compared to previous generations, there’s something about the rawness of facing that concept made flesh that shifts the terms of debate.

Here come the furious children of the Cameron years, now finally old enough to make it to Westminster. The new intake includes a handful of the first generation to have their formative years shaped by his government, boomeranging back into the heart of the institution where harsh choices were made, including the tripling of tuition fees. They have very little power to change anything still, since the scale of Labour’s defeat at the last election means they lack the parliamentary numbers or the winning mandate. But these ghosts of decisions past are proving rather good at rattling their chains.

Scrapping tuition fees for everyone, as Sultana seems to want, remains a poor way of helping more working-class kids go to university; it overwhelmingly benefits the middle-class families whose children still dominate higher education, and doesn’t tackle the deeper rooted reasons that poorer families miss out. But it’s a lot harder to make that technical argument once a generation who racked up five-figure debts to get a degree starts entering a parliament full of people who mostly went for free, and who suddenly find their moral authority evaporating as a result.

Facebook Twitter Pinterest ‘Age is the yawning divide between newcomers such as Nottingham East’s Nadia Whittome and many of the ministers they’re facing across the floor of the Commons.’ Photograph: Ollie Millington/Getty Images

The truth is that Generation X graduates got lucky, and luck is never fair. We were simply born at what we didn’t know then was the right time; early enough not to get caught by the introduction of fees in 1998, but late enough for universities to have started expanding a little, taking in not just old Etonians but kids like me who were the first in their families to experience higher education. And it wasn’t just the debt – although arguably it more closely resembles a graduate tax – that we managed to duck.

We didn’t have the gnawing anxiety I see in students now, who can’t afford to miss a single lecture; who spend their holidays frantically chasing internships, because they want to get good enough jobs to make it all worthwhile. Tuition fees haven’t just shaped their finances, they have shaped the way they live their daily lives.

There was nothing malicious about what the lucky generation did, of course, in taking advantage of what was freely given. But we did nothing much to earn that luck either, any more than many of us earned the happy accident of graduating when jobs weren’t so hard to come by (at least compared to the stagnant years following the banking crash) or flats in London were still just about affordable. It was just a good time to be young. But it’s left us without much of a leg to stand on.

Unfortunately for everyone concerned, the facts of higher education finance haven’t changed. The biggest practical obstacle facing poorer students arguably isn’t debt, but the fact that they are disproportionately less likely either to do A-levels or to achieve the best grades. Tackling that means ploughing cash into closing the gap from early years education onwards, plus more use of lower offers for kids who have overcome considerable odds to get a B – although the new student quango, the Office for Students, is currently reviewing the case for what it calls an even more radical approach to shaking up admissions.

There’s a separate philosophical argument to be had about whether higher education is such a universal good that the state should pay for everyone to access it, of course, but even that will come up against the pressure to prioritise in what are likely to be lean times post-Brexit. If I could bring back one thing from the 1990s it wouldn’t be free tuition but means-tested maintenance grants to cover student living costs, so the young people whose parents can’t afford to subsidise them well into their 20s don’t feel forced to go straight out to work.

Hovering in the wings, meanwhile, is the Augar review commissioned by Theresa May, now sitting on Johnson’s desk, arguing for major investment in further education (which overwhelmingly would benefit working-class kids) and cutting tuition fees to £7,500. (Although that isn’t enough to close the unfair gap emerging between students whose parents pay upfront, so that they never have to enter the loans system, and those who graduate owing more than they are realistically going to repay.)

But no technical policy fix can solve the tricky political problem that the new parliamentary intake is highlighting – which is that, as every parent knows, “do as I say, not as I did” is a spectacularly unpersuasive argument. Get lucky, and you lose the moral high ground from which to deny that same luck to others. The trouble with getting anything for free is that, sooner or later, there ends up being a bill to pay.

• Gaby Hinsliff is a Guardian columnist