I have spent the past four years devising ways to win hearts and minds for poetry and am now expert in how not to do it. Anyone giving away free books of love poems in a public place will inspire only wariness and quickened steps. Anyone pressing poetry on the queue at the deli counter at Waitrose in Westfield’s White City shopping mall will wish she had never been born. Many months after encouraging the supermarket to enlist a lively young poet to offer a poem-on-demand service with takeaway lunches on National Poetry Day, my embarrassment is so deep that I’m still unable to buy milk there. Personally I did little for poetry that day: still less for sandwich sales.

This year marks a new beginning, provoked by a line in the film The Big Short. “Truth is like poetry. And most people f***ing hate poetry”.

As I joined in the cinema audience’s knowing laughter, something clicked. The whole evangelical look-lovely-poems-are-good-for-you schtick assumes poetry is a precious endangered superfood, somewhere between a vitamin pill and a rare flower.

Wrong. It should be ranked among life-forms that will survive nuclear holocaust: jellyfish, cockroaches, Millwall fans.

Any effective campaign promoting poetry needs to distil this toughness and ask: what immunity does this awkward art carry deep within it that resists eradication? What force lives in a form in which language, selfish as a Dawkins gene, deploys all its armoury to demand space, seize attention, burrow tenaciously into memory?

Yemen, where agents of Isis and al-Qaeda use poetry to recruit suicide bombers, has one answer:  prisons where I’m told poetry’s the genre most frequently nicked from the library , have another. The German legal system has recently been rocked by a poem suggesting the President of Turkey enjoys sex with goats: on its own terms  – “this-is-an-actual-poem-not-an-inadvertent-tweet-so-sue-me” – it must be counted a success.  In Qatar, poets have two routes to fame: they can enter television talent shows called Million’s Poet and Prince of Poets, or they can be whipped, incarcerated and – occasionally, after back-room deals and international outcry – granted royal pardon. In troubled places, where massacred infidels outnumber daffodils, poetry matters. And not in a good way.

Closer to home, where the charity I run invites foundations and funding agencies to support National Poetry Day in the UK, I am still – nearly four years in – working fitfully on the “long-term strategy”, the “case for support” and the “call to action”. There are plenty of off-the-shelf versions available. Poetry consoles. It gives insight into the human condition. It makes men – and women – cry, which is of course A Good Thing, unblocking those constipated emotions. Yes indeed. These are all appealing headline-friendly claims, valid in certain places and at certain times, with advocates in high places: they are frequently applied to the visual arts and music, and can embrace all of culture including gardening, sport and the keeping of pets

But poetry, dammit, is different: anyone who attempts to throw small nets of words over slippery meanings must reckon with the slipperiness of language too. Poetry, in which the unsaids, the gaps, pauses and breaks, the echoes set off by certain forms and phrases, are as significant as the words themselves, has a Houdini tendency to wriggle out of any case-for-support one constructs. All sweeping statements about poetry undermine themselves.

And yet, there must be something sensible to say about the social case for poetry without summoning up images of vitamins. Last week, I finally found it in a pile of statistics on literacy in schools, released annually by the National Literacy Trust. Children on free school meals are more interested in poetry than their more prosperous counterparts. They write more of it. They read more of it. No one has told them to do this, it doesn’t count towards exam success or earn them credits. But in poetry, that escape-artist of a genre, which cocks a perpetual snook at those who enforce the codes of prose, these children – many from households where English is exotic – find an ally. It lets them into language, and to the limits of language. What happens next is up to them.

Susannah Herbert runs the Forward Arts Foundation, a charity that fosters the enjoyment, discovery and sharing of poetry. Its initiatives include both the Forward Prizes for Poetry and National Poetry Day.