Gotcha, as the Sun is surely thinking. Once again, Ed Miliband has been done up like a kipper by the tabloid of choice for the struggling low-earners he seeks to represent. And this time it’s not for going along with one of its patriotic publicity stunts – as when he posed with its World Cup front page – but for refusing. Asked on a crazily busy day to be photographed wearing a Help for Heroes charity wristband, he failed to do so, and was duly patriot-shamed.

Admittedly, it could have been better handled. (If you’re not going to play the Sun’s game, fine, but tell everyone why before it does – preferably while declaring undying gratitude to war veterans and making a private donation.) But it was a cheap trick, reeking of that aggressive with-us-or-against-us patriotism that roams the streets looking for anyone who doesn’t fall into step. Nobody should be bullied into wearing something to prove their allegiance to a country, whether it’s a bracelet or a red poppy or a saltire in face paint. And nor, arguably, should they be bullied out of wearing something.

This week, it emerged that a 16-year-old girl has been barred from an outstanding London state school because she insists on wearing the niqab, or full-face covering. Camden School for Girls is famous for turning out strong-minded young women but says it can’t teach this one due to an established policy of challenging “inappropriate dress which offends public decency or which does not allow teacher-student interactions”. Hundreds have already signed a petition protesting that what you wear “does not affect anyone else”. And just as the Sun row isn’t really about a bracelet, this isn’t purely about a scrap of fabric worn by at most a tiny minority of Muslim women. The veil is a metaphor not just for the struggle between religious faith and feminism but for deep contemporary fears of division and distance, of the shutters coming down between one culture and another.

It’s helplessly confusing for liberals, who can’t decide which is worse: a Muslim culture where it’s accepted that men will ogle women, and that women should hide themselves for shame, or a western one where girls choosing the veil in defiance of their families, as an expression of their own identity, get lectured by grumpy white men who think they should make more effort to fit in? More surprisingly, even Ukip is baffled by the burqa, veering between wanting to ban it and worrying that, as libertarians, they shouldn’t be banning anything.

Yet we expect headteachers to navigate this impossible terrain, under pressure as they are after the so-called Trojan horse scandal to reinforce something mysteriously known as “British values”. And like it or not, as any ageing former punk knows, clothing does sometimes express values. The unspoken fear must be that if schools surrender on veils, the next thing will be demands for girls to sit separately from boys, or to drop music and sport.

Not, it should be said, that this is the school’s argument. Its governors say merely that they need to see their students’ faces to verify identity – which sounds reasonable, although is perhaps as easily managed by getting students to agree to lift the veil if challenged for good reason – but also because, for educational reasons, teachers “need to see a student’s whole face in order to read the visual cues it provides”. And that’s where it gets tricky.

Humans can, of course, learn to get by without all the non-verbal cues on which most of us unthinkingly rely in social and professional encounters. It’s a tiny thing, but I’ll never forget watching David Blunkett enter a meeting and extend his hand for a handshake at precisely the moment his sighted host did so. Clearly, he was used to strangers forgetting that the blind can’t see an outstretched hand. But when his host twigged, blushed and silently lowered his hand the uncanny thing is that Blunkett was one step ahead of him. He caught the other man’s hand at exactly the right point on that mortified, invisible arc. But imagine the effort and the years of experience that takes. And now ask yourself how long it could take a teacher to learn to decipher, from the droop of a shoulder or half-audible sigh, whether a child is feeling bored or engaged, struggling or racing impatiently ahead, inside that mysterious tent.

It would seem wrong for schools not to warn girls that by barricading themselves behind yards of cloth they’re potentially holding themselves and their learning back, shutting down future opportunities in much the same way as a disruptive child who blanks the teacher; and that while what you wear certainly shouldn’t affect other people, sometimes in practice it just does. But it’s precisely this question of future opportunities that makes a ban on niqabs in all schools feel instinctively wrong.

It’s not hard to understand why Jack Straw, who first raised the veil issue, felt uncomfortable seeing shrouded constituents in his surgery: most of us instinctively interpret concealment as a hostile, alienating thing, as uncomfortable as talking to the back of someone’s head. But the rule of thumb must surely be that we all have the right to dress or speak in an alienating, even offensive way so long as we do no harm.

If you’re a doctor who puts patients at risk of cross-infection by moving from bed to bed while wearing the same bit of dangling cloth, then whether that’s a veil or an old-fashioned consultant’s tie you can legitimately be asked to choose between clothing and career. If you’re bearing witness in court, justice for the defendant is best served by letting jurors evaluate your expressions. The state can expect women to reveal themselves where concealment exposes others to risk.

But constituents shouldn’t have to dress to make their MP feel comfortable in order to get help in a crisis. Women reluctant to undress for a male doctor should be able to see a female one. And if a girl wants to learn in a profoundly empowering school that prides itself on fostering independent thought, then it feels wrong to push her away, possibly into an establishment without half as many principles. It’s a properly liberal education that sets girls free, or they wouldn’t risk death in countries from Pakistan to Nigeria to get one. We should do nothing to exclude from it those who may one day need it most.