People who like banning things, should be banned from doing so. Discuss. And no, it’s not an A-level philosophy question. It is the essence of the argument the higher education minister Jo Johnson started this week, when he announced that universities who don’t protect freedom of speech on campus could be fined.

It was preposterous, he said, that someone like Germaine Greer could be no-platformed when “she has every right, if invited, to give her views on difficult and awkward subjects”. (Greer’s invitation to give a guest lecture at Cardiff University was famously challenged by its women’s officer, who accused her of transphobia, although it eventually went ahead). Fostering “healthy disagreement” and challenging conversations was, Johnson insisted, what universities are all about.

The idea of zero tolerance for liberal intolerance will be wildly popular with the sort of Tory who spontaneously combusts at the word “safe space”, and doubtless with the anonymous Cambridge don who told the Times his students seem determined to “exclude anyone who challenges them”.

But the practicalities are baffling, and not just because of the fiendish difficulty universities face in making their student union activists fall into line. How does all this mesh with a Prevent anti-terrorist strategy requiring universities to keep out extremist speakers? Perhaps there will be a banned list for Prevent, and another list of those whom students are banned from banning.

And it’s hard to see how fines would help with the kind of intense ethical dilemmas US universities are now facing, following increasingly violent clashes between far-right speakers and protesters on campus. Florida declared a state of emergency after white nationalist Richard Spencer was invited to speak at the University of Florida on Thursday, bearing in mind the recent death of a young woman who was protesting at a far-right rally in Charlottesville.

But universities are caught between a philosophical rock and a hard place, between the right even of obnoxious individuals to freedom of speech and students’ right to freely protest. The university’s president, Kent Fuchs, admitted before the lecture that academia was still wrestling with its response, but hoped many of his students would simply stay away. Anyone is free to speak, but not everyone is entitled to be heard.

Both British and American universities are now grappling with a fundamental clash of cultures, pitting an older generation of liberals who believe free speech should be protected at all costs against a younger generation that is both quicker to take offence and, crucially, much more anxious about giving it. Going back to speak to students at my old university last year, I was struck less by a zealous desire to police speech than by their desperation to avoid hurting other people’s feelings by displaying even inadvertent prejudice. They came across not as hysterical snowflakes, but as earnest and thoughtful.

As ever with student politics, it’s the ridiculously self-important extremes – like Oxford’s Balliol College demanding the Christian Union be barred from a freshers’ fair because Christianity was “an excuse for homophobia” – that make headlines, even if that’s not how most students think.

But it’s clear nonetheless that free speech now risks joining capitalism and democracy on the list of ideas older people absolutely take as gospel, and whose merits younger people increasingly don’t see. As with capitalism and democracy, bellowing that the kids are stupid and wrong is likely to be less successful than asking why students don’t value something that is precious to their parents for good reason.

Students have grown up watching the far-right systematically exploit online freedom of speech to organise, and then to achieve political breakthroughs

This generation of students grew up as guinea pigs in arguably the biggest experiment in untrammelled free speech in a century. The founding principle that anyone can say what they like on the internet has been both a force for good – giving dissidents in totalitarian regimes a voice, or most recently empowering women to expose the extent of sexual harassment using the #metoo hashtag – and a powerful force for ill. Bullies have so many new ways to silence, belittle and intimidate; so many thrilling opportunities to threaten violence against anyone whose opinion they don’t like. For every Arab spring nobly facilitated, there are thousands more toxic episodes of teenage bullying on Facebook, or Twitter pile-ons led by people old enough to know better. It’s exhausting for adults, never mind teenagers whose self-esteem is fragile.

Teaching kids to have faith in the power of righteous argument to defeat evil, meanwhile, is vital to the functioning of a healthy democracy. But it’s a tough sell when they’ve seen Hillary Clinton lose after elegantly out-debating Donald Trump, or the remain campaign outwitted by a fib on a bus and some racially charged posters.

They have grown up watching the far right systematically exploit online freedom of speech to organise, and then to achieve political breakthroughs which loom threateningly large over millennial lives. Mob rage on campus against speakers like the writer Charles Murray – the infamous proponent of the idea that IQ is closely linked to race and class, whose recent appearance at a college in Vermont ended in masked protesters clambering on his car and pounding on the windows – shocked even liberals who have loathed Murray’s views ever since his book The Bell Curve was published in the 1990s.

And if they learned young that free speech has a dark side, crucially this generation has also learned that the advantages of it are not equally shared. It’s women, ethnic minorities and LGBT people who get the disproportionate share of abuse online, and anecdotal evidence suggests it’s men who do much of the trolling. The fact that women are twice as likely as men to support a regulated internet, according to a recent report from thinktank Policy Exchange, may well reflect the fact that they’re more often on the sharp end of behaviour that might need regulating. Meanwhile, the most zealous free speech advocates today aren’t kindly liberals fretting about the free exchange of ideas, but alt-right thugs from Breitbart.

So in that sense, Johnson is right to make a case for open debate that for once doesn’t come from fans of Katie Hopkins. He’s right that this newly censorious mood on campus is potentially unhealthy and that the principle of free speech, subject always to not shouting “fire” in a crowded theatre, remains sacred – which is why universities have long had a statutory duty to uphold it, albeit mainly for the benefit of academics whose research leads to uncomfortable conclusions.

The ideal is as important as it ever was. But it can be hard for millennials to see that, when their everyday experience is of the strong using online freedom of speech to bully the weak. What universities need from the outside world isn’t fines, but help in showing that censorship can be just as dangerously abused; that blocking arguments you don’t like doesn’t make them go away; and that debating issues face-to-face in a controlled environment is still the best way of thrashing them out. If we want students to crawl out of their safe spaces, their elders must think rather harder about what made them feel so unsafe in the first place.

• Gaby Hinsliff is a Guardian columnist