'We have made Italy, now we must make Italians" – thus the old saying. Today we have made the euro and the crisis of the euro is unmaking Europeans. People who felt enthusiastically European 10 years ago are reverting to angry national stereotypes.

"Hitler-Merkel" said a banner carried by young Cypriot protesters earlier this week. Next to those words there was an image of the European flag, its yellow stars on a blue background now angrily crossed out in red. Sweeping negative generalisations are heard about "north" and "south" Europeans, almost as if these were two different species. Yet what historian could seriously maintain that Milan has more in common with Nicosia than it does with Nice or Geneva? Even highly educated pro-Europeans say things in public about other nations that a decade ago they would not even have thought, let alone expressed. As parts of Europe became more anti-German so parts of Germany became more anti-European. A vicious spiral looms into view, like a twister on a rural highway in the American midwest.

We should note with relief what has not happened – or at least not for the most part and not yet. With the exception of neofascist parties such as Golden Dawn in Greece, European rage has not been turned against immigrants, minorities, and imagined fifth columns. Germans do not blame their woes on rootless Jews, Muslims or freemasons; they blame them on feckless Greeks. Greeks do not blame their woes on rootless Jews, Muslims or freemasons; they blame them on heartless Germans.

Nonetheless, this is bloody dangerous. To be sure, 2013 is not 1913. Germany may be calling the shots in the eurozone, but it never sought this place in the sun. The German people were never asked if they wanted to give up the deutschmark – the answer would have been "no" – and roughly one in three of them now say they would like to return to it. In saying this, they profoundly misunderstand their own national economic interest, but that's another story.

The EU as a whole is the most reluctant empire in European history, and Germany is a reluctant empire within this reluctant empire. The risk of interstate war in EU Europe is tiny. (The 1913 analogy is more applicable to Asia today, with China taking the part of Wilhelmine Germany.) There is, however, a real danger that the bonds of sentiment and fellow-feeling essential to any political community are being rent asunder.

Remember that for countries like Cyprus the worst is yet to come. I hesitate even to raise the spectre – to "paint the devil on the wall", as one says in German – but what if some unemployed and mentally unbalanced Greek or Cypriot youth were to take a pot shot at a German politician? With luck, the shock would cool the overheated rhetoric and bring all Europeans together. But we should not wait until a shot rings out.

Why are we in this downward spiral of mutual resentment? Because of the basic design flaws of the euro, certainly. Also because of mistaken economic policies in some of the so-called peripheral countries of the eurozone and – more recently – in the northern core. (As I explained in this column a fortnight ago, the big problem with German policy is not what it asks others to do but what it does not do itself. It should help adjustment across the eurozone by boosting its own domestic demand.) Meanwhile, each short-term eurozone fix sows the seeds of another eurozone crisis. Thus, for example, a 50% haircut for holders of Greek government bonds, agreed in autumn 2011, helped topple Cypriot banks into the abyss.

Yet the deepest cause is the mismatch between a single currency area and 17 national polities. The economics are continental, the politics are still national. What is more, those politics are democratic. If this is not 1913 it is also not the 1930s. Instead of the "Europe of the dictators" we have a Europe of democracies. Instead of Trotsky's "permanent revolution", we have permanent elections. Some leader somewhere in Europe is always having to trim the jib and pull in the mainsail because of an imminent vote. This year, it happens to be Angela Merkel, whose general election looms in September. Every one of the eurozone's 17 and the EU's 27 national leaders thinks first of their national politics, media and opinion polls. Tempting though it is to say: "We have made Europe, now we must make Europeans," the truth is that in this respect we have not made Europe.

So what is to be done about these politics? An ingenious Italian professor, Giorgio Basevi of Bologna University, recently sent me a proposal for alleviating the problem by synchronising national and European elections. It's a brilliant idea and, of course, a total nonstarter. Tell that to the electorates of Europe! Others suggest that the next president of the European commission should be directly elected, perhaps with candidates nominated by each of the main party groupings in the European parliament. Well, why not? But if you think this will make unemployed Greeks and resentful Germans suddenly become all warmly pro-European again, you need your head examined.

For now, there is simply no substitute for national politicians going against the wind of their national public opinions to explain, in their own national languages and idioms, that – according to place and need – Greeks are not all feckless spendthrifts, Germans are not all heartless Teutons, and so on. They it is who must seize every opportunity to enlarge on why, even if we are cold and wet in the European boat, we would be even colder and wetter in the water.

And if it takes a new enemy? As an ethnic scapegoat acceptable to almost all continental Europeans I would usually be happy to suggest my sterling compatriots, the English. (We are used to it. We can take it.) But whatever else you may load on the English, you can't blame them for the shemozzle of the eurozone.

Twitter: @fromTGA