On 1 February 1960 Franklin McCain and three teenage friends from the historically black North Carolina Agricultural and Technical College, went to the whites-only counter at Woolworths in Greensboro and took a seat.

They were not part of an organisation and had never been politically active before. "I don't think the [established civil rights groups] really understood what the driving force was for this movement," McCain says. "We had four kids here trying to address an unequal system. Just four kids who were somewhat introspective."

The night before they had stayed up until the small hours goading each other into action. They didn't warn anyone because they thought adults would try to talk them out of it. Their attempts, the next day, to get a few people to join them failed. "We just thought it was useless waiting for them to catch up. We didn't have the time to convince people … People needed to believe in it enough to die, they had to walk on the picket lines until their shoes wore out. We wanted to go beyond what our parents had done. And we had nothing to lose."

McCain describes the feeling of sitting at the counter – confronting the oppression of ages as a cop brandished a stick he could not bring himself to use – as one of zen-like serenity. "I had the most tremendous feeling of elation and celebration. I felt that in this life nothing else mattered. Nothing else has even come close. Not the birth of my first son nor my marriage. I had no tensions and no concerns. If there is a heaven, I got there for a few minutes."

And so, from a moment of tranquillity began a turbulent decade of student-led activism, both locally and globally, that produced some of the transformative movements of the last century. The 60s did not invent student radicalism. But it did witness a spike in a centuries-long tradition that has ebbed and flowed from 19th century Russia to Soweto and is surging once again across Europe.

Last week alone saw a wave of occupations and demonstrations in Britain, widespread disruption in Italy as train lines and motorways were blocked, and clashes between Greek students and police outside parliament in Athens.

As these protests intensify – as they are bound to – we can expect them to be routinely disparaged on the right as either privileged kids acting out or innocents led astray by revolutionaries. But there is also a risk that, either through nostalgia or wishful thinking, they might be misunderstood by the left.

There is nothing intrinsic to being a student that makes them radical. Like everyone else their politics are shaped by time and place. During the 1926 General Strike in Britain students were used as scab labour. In Venezuela, they are as likely to be against Hugo Chávez as for him. I entered university four months after Thatcher's third victory and graduated three months after Labour's fourth defeat. It is not surprising students were, if anything, quite conservative.

That students and youth in Europe have erupted at this moment, however, should come as no surprise. More than one in five people under the age of 25 in the EU is unemployed. In Spain the figure is 43%; in Greece 30%; in Italy 26%. Meanwhile the principle that education is a public good, to which all are entitled, all contribute, and all benefit through a more competitive economy, is in its death throes.

In the name of meritocracy Italy is about to slash €26m from its scholarship fund. The British government's latest proposal, giving anyone on free school meals a year's free tuition, is like trying to tackle poverty by cutting coupons: inadequate and ineffective. I would have qualified for that and there's still no way I could have afforded to continue at university.

Nonetheless, there are elements of McCain's recollections that do reveal a propensity among students and youth to militancy. They are more likely to have time, energy, ideas and ideals, and more likely to fight for them because they probably don't have a stake in the system as it stands. Like McCain and his friends they are less likely to have been either worn down or, worse still, corrupted by established institutions and as a result more likely to be passionate, impatient and proactive. It is no surprise that the National Union of Students and the Labour party have kept these ongoing protests at arm's length. Indeed, given their record to date it is hoped that, since they have proved unable or unwilling to lead, they will at least follow.

This is all too easy to dismiss and disparage as a toxic cocktail of naivety and privilege. Such sleights are flawed. First, in Britain at least, the notion of students as a wealthy strata on a three-year hiatus from real life is outdated. A third of students in higher education are from working-class or lower-middle-class backgrounds, and work during term time to pay for basic needs and books and equipment. Just under one in five of those with jobs works more than 17 hours a week. One in five lives at home. Add further education and school students into the mix and you have a demographic that looks more like the characters in The Office than Brideshead Revisited.

Second, even if they were middle class, so what? Beating up on the middle-class does not help the working-class. Indeed, by eliminating the notion that education is a public good you eradicate the primary means by which working-class people can better themselves. They are not just an attack on finances, but on aspiration.

It can never be pointed out too often – if only because it is so frequently ignored – that this situation was not created by excessive public spending but by an international banking crisis brought about by an unregulated binge in the private sector. In a sordid redistribution of wealth from poor to rich, working-class kids will be denied the possibility of a university education because wealthy traders were in denial about economic reality.

So while it's true that others have it worse than students, it also entirely misses the point. Protesting against tuition fees is not a sectional interest. For most, student years mark a transition from youth to adulthood, which means the burden for these increases do not just fall on individuals but families – who will already be suffering from the crisis in others ways. Thatcher's cuts blighted isolated communities, whether they were pit villages or northern cities. These attacks are not just deeper but broader. Clearly, how students' resistance to these cuts pans out will have ramifications for successful opposition to the entire austerity programme. That is reason enough to deserve our support.

But while students can be the spark for the broader struggles ahead, history tells us that they are unlikely to be the flame itself. Students and the young might be the most likely to protest, but they are among the least likely to vote – if indeed they are even eligible to vote – and cannot withdraw their labour to any devastating effect. McCain's stand gave courage to the sharecroppers and domestic workers; the French students in 1968 bolstered the confidence of factory workers. The threat British students pose – much like the financial crisis bringing them on to the streets – is of contagion. That their energy, enthusiasm, militancy, rage and raucousness might burn in us all.