Britain’s government shows little sign of worrying what fellow EU members think of it. As a lukewarm Remainer, Theresa May kept her head below the parapet; as a born-again Leaver, she won’t be left behind by her hardliners. And so she’s placed them in (notional) charge of Brexit.

Domestically, it’s understandable. Remainers can’t agree on tactics. Leave leaders push for the most brutal Brexit possible, with plenty of support from the Tory back benches. ‘Liberal Leavers’ find themselves marginalised. May has no need to fear Jeremy Corbyn (whose heart isn’t in this fight anyway); for now, her greatest threats sit behind her. Whose agenda is she likely to back?

So Brexiters hope the EU-27 will simply roll over and offer Britain nearly all its preferred benefits with almost none of its perceived obligations. Mutual interest (defined in British terms) will win out, they say. They mistake the balance of power in the negotiations. They give needless offence and encourage partners to rally against us. Above all, they misunderstand the politics and psychology of the Union they want to leave.

First: ministers argue that as the UK has a trade deficit with the EU-27, the EU-27 has more interest than we do in making British trade no harder than it is now. Leave the mercantilist nonsense that trade is a zero-sum game to one side; just note that 44% of British exports go to the EU-27, while only 8% of EU-27 members’ exports go to us. Note, too, that not all EU members suffer equally from Brexit. And EU-27 trade matters more to other members (yes, including Ireland) than trade with the UK.

Second: some anger with Britain is inevitable. The EU-27 feel rejected; divorce is ugly; human nature and wounded pride conspire against easy goodwill. But because Tories are only talking to British voters and virtually ignoring the continent, we’re rubbing salt into the wounds. May’s stridently nationalist conference speech left the rest of Europe aghast. Calling free movement’s central status a ‘total myth’ and ‘bollocks’ is as offensive as it is inaccurate.

But third and above all, May makes a cardinal error in diplomacy: she assumes the rest of the EU thinks as Britain does. In the end, Britain always treats the EU as a transaction – a trade-off of sovereignty for pragmatic ends. Sure, it doesn’t just think it’s about the money (though let’s face it, it does mainly think it’s about the money). But with few exceptions, British ministers never bought into ‘Europe’ as an ideal. Cameron gloried in his refusal to do so.

It would be absurd to say other governments have no transactional interest in the EU. But it’s not the whole story. Other members believe in the European idea (or at least are invested in it) in a way Britain never really did. The original six members remember what three Franco-German wars in 70 years did to Europe. Spain, Portugal and Greece (yes – despite everything, it doesn’t want Grexit) remember military dictatorship and their journey to the EU afterwards. Eastern European countries remember the two vicious world wars and their communist past, from which they escaped only recently. A Polish foreign minister told his British audience so in no uncertain terms in 2012:

Do not underestimate our determination not to return to the politics of the 20th century. You were not occupied. Most of us on the continent were. We will do almost anything to prevent that from happening again.

This shouldn’t be so hard to understand. Britain voted to leave the EU in the face of the economics. Anti-Europeans glory in Britain’s uniqueness. Leavers complained bitterly about ‘political union’. Why, then, can they not grasp that our partners see things differently and won’t put sales of prosecco above the integrity of the European project? How can they not see that Angela Merkel – the daughter of a Lutheran pastor who grew up in atheistic East Germany, who knows the terrible German history which gave birth to the EEC and understands what recently-won freedom means – will (rightly) put the EU above exporting Volkswagens?

British people often object at this point. Why, they ask, can’t a project built for peace and democracy survive without deterring people from leaving it? Well, saying countries which participate in EU projects need to follow the relevant rules is actually pretty reasonable. The EU also legitimately fears the unstitching of the single market if every country can unpick anything it dislikes. But more importantly, the critics are confusing belief in an ideal with blind faith in human nature.

The EU stems from memories of the old Europe, of how low nations and people could sink – from fear, at least in part, of the dark heart of man. Scepticism about human (or unconstrained nation-states’) nature and idealism about the European project are inextricably linked. It’s a precious achievement built not on faith in human civility, but on the need to curb human barbarism. The EU-27 fear for the survival of their project. That obviously stems partly from its many problems. But a nervousness, a belief that something so painstakingly built could easily fall apart, is a feature of European integration – not a bug.

As populist, xenophobic authoritarianism crashes over the West, the EU-27 will fear a return to the darkness all the more. I understand their fear, because I share it. Britain deludes itself if it thinks its faith in balance sheets will come out on top.