That isn't the terrible disaster that the hand-wringing opinion pieces would have you believe. A society's pedagogical needs change. Sometimes we need to remember, however, that there are reasons for learning extinct languages beyond boarding-school nostalgia or a burning desire to get into the Tory cabinet.

Considering that Arabic or German could be your ticket straight out of the jobcentre, the suggestion to learn a dead language might sound insane. For many reasons – commercial, diplomatic, intellectual – we need to wake up to the awkward reality that monoglottism is bad for us. The British are the dumb men of Europe and it is embarrassing. So, go ahead – learn a modern language. If you want to be obvious about it.

But all sorts of "dead" languages enjoy important existences today, albeit in quieter, more subtle ways. They're threaded almost invisibly through contemporary culture, kept in shape by a combination of tradition and devotion, like good hand-stitching.

There are practical reasons for learning an extinct language. It can make acquiring second, third, even fourth languages easier. Linguists map languages on to family trees. In the Indo-European language family, groups as seemingly disparate as Indo-Iranian and Balto-Slavic descend from a lost parent language called Proto-Indo-European. So, according to the same principle that your great-grandfather had children and grand-children and great-grandchildren, learning a language that occupies a place farther up the family tree will mean that younger languages will have grown up out of it.

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This argument is often used in defence of learning Latin, which is parent to French and Spanish, among others (it doesn't apply to Ancient Greek, however, whose offspring are few).

Some dead languages are more dead than others. Languages whose writings are beloved never really die. Old English will be with us as long as we treasure Beowulf. While our fascination with King Arthur rumbles on, Old English's inheritor, Middle English, survives. Middle English romance tales of the kings, queens and chivalric heroes of Britain are woven into the stories we still tell our children, while film studios seemingly never tire of adapting them. Show me a lover of televised dragons and I will show you a fan of medieval literature.

Learning a medieval language – maybe Old or Middle English, Old Norse, Old French, or Occitan – connects you to a body of literature which is at once intensely familiar and delightfully strange. These languages gave voice to the foundation-stones of European literature, but understanding them takes a fight. It is an uncannily lovely experience to read lines written many, many hundreds of years ago about bits of the world that you could have laid eyes on yourself.

If you've ever taken a dejected walk alone along a frozen clifftop, you'll thrill to the Old English elegy we call The Wanderer, in which a wineleas guma (friendless man) gazes miserably out over the hrimcealde sæ (ice-cold sea) as he treads wræclast – the path of exile. It makes The Smiths feel inevitable.

On that note of Britishness, however, the case for dead languages hits a specific bump in the road. Thus far I've been discussing vernacular languages, but the arguments stand for the classical languages – Latin and Greek. But there is no getting around the fact that, in contemporary Britain, the study of Latin and Greek is not just a matter of battling the gerundive.

The 'classics' are indivisibly attached to class difference. No matter how many state schools take it up, Latin and Greek have historically been the preserve of feepaying schools, Oxbridge candidates and, ultimately, the ruling elite. We may see the Roman and Greek world in television history programming and in blockbuster movies, but we read their words inscribed on the walls of buildings where power reside. If classical languages weren't already associated with very posh people, this chunk of bluster by Boris Johnson ought to have done the trick.

What's the solution? Well, education reform is obviously beyond the reach of the lucid at the moment. We might as well start with a change in the way we think about extinct languages.

Begin with the easier ones, the ones closer to the tongues we speak today. Working back through the stories that you have grown up loving without even realising it, you'll be surprised by how quickly you can slip into easy conversation with the voices of the European past. Start with the gorgeous Middle English lyrics, perhaps, looking words up in the Middle English Dictionary. Follow what leads you find there.

Or, if you're feeling very ambitious, go in a different direction up the Indo-European family tree and take some Sanskrit classes. It is older than either Latin or Greek, but related to both. Since the discovery of the Indo-European language connection in the late eighteenth century, Sanskrit played an important role in European comparative linguistics and thus was taught in British universities. Although it is certainly still academically alive, Sanskrit no longer has the vogueish status it enjoyed in nineteenth century Britain.

If you're interested in Indo-European linguistics but Latin and Greek feel politically alienating or perhaps just plain boring, you could do much worse than learning – or sending your child to a school that teaches – Sanskrit. Its contemporary Indian language descendants have played a big part in British history, after all.

We make many ill-thought-out assumptions about "dead" languages. People are forever throwing out truisms about the "logical" nature of Latin while not knowing much about it, or casually deriding things as "medieval" when they aren't at all (cf: witch-burning). Stop watching Game of Thrones. Beowulf is better and features less rape. Do it for the sake of your language skills, do it to connect with the past – but above all, do it because the literature is beautiful.

Josephine Livingstone