What does the EU want? This simple question has foxed Brits throughout the Brexit talks. It is alleged that Brussels is desperate to retain Britain; that it yearns to get rid of it; that German car-makers and friendly states such as the Netherlands will force Angela Merkel to let Britain cherrypick the best of membership; that Europeans want to ruin Britain, sending it on its way with a punishment beating pour encourager les autres. None of this contradictory speculation has turned out to be right, and Britain’s negotiating efforts have been the poorer for it.

European mainlanders can be hard to read. The Friday before last, prominent Germans including Annegret Kramp-Karrenbauer, Angela Merkel’s heir presumptive, wrote a saccharine letter to the Times urging Britain to stay. On Monday the Polish foreign minister broke EU ranks to suggest that the Irish backstop be limited, to get Theresa May’s deal over the line. Yet on Wednesday Merkel seemingly contradicted her own colleagues, opining fatalistically that Britain, an island, had always had “patchy” relations with the EU and suggesting that its exit is inevitable. The day after, an exasperated Emmanuel Macron told a crowd near Lyon that Brexit has “torn British society apart” and “cannot be delivered”, his tone so critical that it moved a Spectator writer to ask why the French president “hates Britain so much”. The motivations and instincts of our continental partners sometimes baffle us Brits.

To un-baffle ourselves, a useful principle is that most of what the EU and its leading members say or do can be traced back to the quest for the quiet life. Brexiters can forget their theories about Teutonic desires to rule the continent. Remainers can abandon their theories about Europe as a “peace project” per se. The reality is at once more prosaic and more poetic than either side allows: the European project knows no higher ideal than calm good living.

The EU and most of its states were born or reborn from the rubble of war and the traumas of totalitarianism

That applies to the Brexit talks. The remaining 27 member states of the EU are fed up of the time- and energy-sapping annoyance and want it sorted, be that through the passing of May’s deal, a speedy British pivot to the “Norway” option or a decision to end Brexit altogether. In Brussels it is now wearily assumed that Britain will request an extension to the article 50 negotiating period. The officials’ nightmare is that this will drag on into the period of the new European parliament from July, which may require Britain to hold its own European election, or that Britain will withdraw article 50 only to trigger it again soon. “Stay or go, just make your minds up!” is a typical entreaty.

Europe’s quest for the quiet life goes much further. The EU and most of its states were born or reborn from the rubble of war and the traumas of totalitarianism. Britons forget how deeply that affects their instincts. History is dense, present, complicated and inescapable on the mainland in a way that it is not in Britain. The pavements of German cities are studded with brass plaques bearing the names and dates of those deported to the death camps, planted outside the addresses where they once lived. Memories of flight, destruction and oppression – the 3am rap at the door, the rumble of military trucks on cobbles, the squelch of carts laden with possessions on muddy tracks – live on in continental families in a way that they do in comparatively few British ones.

The opposite of horror and cataclysm is the quiet life. Voltaire wrote his novel Candide in 1759 after the catastrophic Lisbon earthquake and amid the destruction of the Seven Years’ War. The book preaches neither Panglossian optimism nor head-in-hands gloom, and rather the stoical satisfaction of a peaceful plot of land providing for its owners’ needs under the maxim: “We must cultivate our garden.” In the shadow of horror and cataclysm, the modest goal of a happily cultivated garden is the height of decency and civilisation. More than grand rhetoric about continental unity or geopolitics or European culture, this is the real objective of the EU – and what holds it together. It is also the thing that Brits most struggle to understand.

The European Coal and Steel Community, the EU’s first precursor, was launched in 1952 to make the weapons-building parts of the French and German economies interdependent. The Treaty of Rome in 1957 was designed to make war between the two inconceivable. Having built peace, the next step was prosperity. The early European project underwrote the postwar boom, and with it welfare states promising material good living but also immaterial totems of the European lifestyle such as long holidays and universal healthcare.

This European dream is glimpsed not in luxurious ceremonies in Paris, Brussels or Berlin but in well-heated social housing blocks in Utrecht or Vienna, in comfortable houses with gardens on the outskirts of Barcelona or Prague, in safe streets and decent hospitals. The eurozone crisis wreaked unnecessary and horrific misery on parts of southern Europe. But one can rightly fume about that and at the same time acknowledge that Europe still constitutes the largest concentration of prosperous, well-insured, long-living, safe and well-rested people in the world. Pity those Africans and Asians who would like to join in but are held back by Europe’s draconian immigration laws. The garden has high walls.

The EU’s unofficial mission is to protect this comfortable, once-traumatised European garden from outside threats. When Helmut Kohl confronted sceptics in his Christian Democrat Union with the case for the euro, notes Alexander Clarkson of King’s College London, he did so primarily not with talk of peace but talk of preserving the European way of life. Today the EU is most effective when it shields its citizens from over-mighty technology firms, negotiates trade deals in a world where its population is proportionately smaller every year, and ventures tentative steps towards common defence forces independent from those of Donald Trump’s America. It lures its neighbours not with soaring rhetoric but with the promise of the quiet life for their citizens. Macedonia’s recent decision to change its name, ending a dispute with Greece and launching itself on the track to EU membership, was ultimately motivated by the desire to join the sheltered European garden.

The obsession with the quiet life also explains the EU’s weaknesses. It concentrates too little on non-immediate security, demographic and industrial competitors outside its borders. It prioritises loss aversion above the uptake of opportunities. It generally values the stability of uniformity above the bracing fizz of difference. It is unremittingly defensive.

Its Brexit talks with Britain have illustrated the best and worst of these traits. Shortly after the referendum, Merkel gathered German business leaders and her European counterparts to agree, in essence, that the risk of a fragmenting EU was the greatest danger to the European quiet life. The consensus she forged has held ever since. Its logic: a suburban tenant in Leipzig or Toulouse or Katowice, with his or her modest house and tidy garden, faces more risk from a collapse of the European project – in the nightmarish event that successive members attempt to replicate a successful Brexit or lose faith in the EU’s willingness to stand by member states like Ireland – than from the economic cost of a disorderly Brexit or the security cost of a Britain less militarily committed to the continent.

A tour of European capitals illustrates this truth. The Dutch may sympathise with the Brits but their prime minister also uses Britain as a cautionary tale of a country whose citizens have lost their appetite for “a good life for themselves and those around them”. Poles may want to bend the rules of the Irish backstop to preserve the quiet life for their immigrant compatriots in Britain but only so far, for Warsaw knows the pain of European fragmentation better than most. Athens and Brussels dislike each other but remain committed to Greek membership of the EU because both fear a destabilising rupture. Macron may rail against Brexit but his real target is Marine Le Pen. Germans may be torn between seeking to stop Brexit by backing a second referendum and managing a messy British exit to get it over with but, like their fellow Europeans, their utmost concern is stability.

Seen from Britain it is easy to spot what divides the EU and harder to identify what unites it, namely the quest for the quiet life on behalf of the citizens of a Europe tired of turmoil. Seen from the continent it is hard to understand the case for a wrenching British flounce or a daring British sally “out into the world” for trade with India and the like. If it wants to find common ground, London should pay less attention to the highfalutin European talk of prosperity, security and power and more to the EU’s underlying object. In other words: Brexit will succeed insofar as it serves the pursuit and preservation of the comfortable European garden.

• Jeremy Cliffe is the Charlemagne columnist and Brussels bureau chief at the Economist