What an irony that free speech should have become a difficult thing to discuss. But it has. For parts of the left, the very slogan “free speech” has become a red rag.

On occasion it can be a cover for chauvinism. Much of the anxiety about “no platforming”, “trigger warnings” and “safe spaces” in universities comes from media pundits who have not been near a college campus in decades. If instead of angsting in an armchair you ask smart student journalists what’s going on, you’ll discover those much-mocked “trigger warnings” don’t stop anyone saying anything, they just give traumatised individuals a chance to steel themselves or, if need be, look away – like a “you may find some scenes distressing” announcement on the news. And when you look beyond the headlines, most of the big “no platforming” rows actually turn out to be cases of “if he’s on that stage, I’m not standing next to him”. Petty? Very likely. But ideas or opinions being censored? Almost certainly not.

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But when I began pulling together an issue of Prospect magazine around the theme recently, it became clear just how deep the divisions on this terrain can be. You could have cut the air of our tiny office with a knife. Half the team instinctively felt that there were real problems with opinions being silenced; the other half felt the whole free speech panic was a delusion of powerful white men.

So I’ve been thinking about why feelings got quite so intense on the free speech question. In some ways, paradoxically, it could be because speech is freer than ever, with Twitter offering everybody an equal chance to publish bucketloads of abuse about everybody else. Very often that abuse is misogynist and racist. But those who get jumped on as transphobic, racist or sexist can feel affronted too – and like they have run up against the limits of free expression.

Another twist is that the real crux of the battle between left and right is often about who gets to say things, rather than what gets said. Wealthy, white middle-aged men still dominate most public discussion. When nobody thinks to do anything about that, it doesn’t change, which is why Afua Hirsch likens free-for-all speech to a laissez-faire market, in which the same old cartels always clean up. If proactive efforts to bring in new voices leave the old white, male stalwarts being called on a touch less often, it’s absurd for them to pretend they are being muzzled.

All of us are shot through with subconscious prejudices. More significantly, we are always at risk of class snobbery

And yet. When it comes to the question of what it is acceptable to say, it’s better to give people a lot of leeway before jumping on them. Just as it is the despised murder suspect who most needs the right to a free trial, the right to speak without feeling inhibited only becomes important when there is something to say that somebody doesn’t want to hear.

This is what the novelist Lionel Shriver is getting at when she condemns a “culture of umbrage” in publishing firms and media outfits. Even if you see such fears as overblown, it’s ill-advised to dismiss them out of hand. Because, rightly or wrongly, most British voters feel the same way. Our YouGov poll found many more voters than not (48% against 35%) felt that there are “many important issues these days where people are not allowed to say what they think”. And by a crushing two-to-one majority (67% to 33%) people reject the idea that more care is needed with language, in favour of the view that “too many people are easily offended these days”. That is a considerably bigger majority than that seen when the same question was put to Americans, in the year they elected Donald Trump. And there is reason to suspect that the resentment could also have political consequences at home: the lead for the “politically incorrect” answer on all these questions is massively bigger among those who voted to leave the EU.

Some will read into these results a hankering for “simpler times”, when racism could be aired without inhibition. No doubt that’s one part of the story. But I think there is something else too. All of us, however “politically correct”, are shot through with subconscious prejudices. We might, for example, be more kindly disposed towards people from our home towns, northerners or people with lower-pitched voices. More significantly, we are always at risk of class snobbery; “It is,” George Bernard Shaw wrote, “impossible for an Englishman to open his mouth without making some other Englishman despise him.” There is precious little policing of this sort of disdain, which might be why some of those on the receiving end of it rage against what they perceive as the greater sensitivity of language around, say, questions of race or gender identity.

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We may be freer than ever to speak, but many people don’t feel it. Why not? Perhaps because the new freedom is too quickly used to brand a person, say, as a racist, an antisemite or a homophobe.

Some people are, and it’s fair to say it. But not everybody who says bad things is a bad person. Often it would be more effective to highlight the flaw in a racist, sexist or a homophobic argument, which the speaker may not be aware of, than to attach a label to the person making the argument.

And however problematic an individual remark from a Margaret Atwood or a Mary Beard may seem to some, when people like this are being decried as bad feminists or bigots something has gone wrong. So the real problem is not that speech isn’t free, but that the freedom is too often used to point the finger. Rushing to do that is rarely a winning, persuasive technique. If we could agree on that then we might, I suggest, remember how to talk about free speech itself as well.

• Tom Clark is the editor of Prospect and a former Guardian leader writer