Most European citizens - more than 60 per cent in France and Germany - believe Turkey should not become part of the EU.
There are various reasons for this opposition - some valid, some based on prejudice: Turkey is too big; Turkish migrant workers might swamp other members; Turkey has a shaky human rights record; Turkey oppresses the Kurds; Turkey has not solved its problems with Greece over Cyprus.
But the main reason is surely that Turkey, a mostly Muslim country, governed by a Muslim party, is viewed as too foreign. In the words of Valery Giscard d'Estaing, the former French president and one of the authors of the EU constitution, "Turkey is not a European country".
This is hard to take for members of the secular, westernised Turkish elite, who have spent decades, if not longer, trying to prove their European bona fides. As one highly educated Turk, working for an international organisation, put it to me recently: "We play football with them, sing songs with them on TV, do business with them, improved our human rights, and democratised our politics. We do everything they ask us to do, and still they don't want us."
That's right, said another Turk within earshot, a fluent English speaker who spent much time in London, worked for non-governmental organisations promoting human rights, and was jailed in the 1980s for opposing the military regime: "I hate Europe. I'm not European, and who needs Europe anyway?"
Good question. While the Greek crisis is tearing at the seams of the euro zone, the Turkish economy is booming. To be sure, "Europe" was for many years a symbol, not just of wealth, but also of liberal politics, open societies and human rights. And Turkish society has benefited greatly from its attempt - not yet perfect, not yet complete - to come up to European standards.
But more and more Europeans are disillusioned with the EU. Far from being a model of democracy, it is associated with an arrogant, out-of-touch mandarinate that issues rules and edicts with paternalistic and high-handed disregard for ordinary citizens. And some of its new members - including Romania, Bulgaria and Hungary - are not exactly paragons of open liberal democracy.
So if Europeans don't even believe in their own union, why should Turkey wish to join it? The woman who protested she hated Europe would still like to see Turkey in the EU. Her venom was that of a spurned lover.
Members of Turkey's secular, pro-European elite, governing almost continuously since Kemal Ataturk founded the republic in 1923, are now being squeezed from two directions. Obstructed by the EU, they are also being pushed from their positions of privilege by a new elite more provincial, more religious and less liberal, but not necessarily less democratic - a cohort personified by Recep Tayyip Erdogan, the highly popular prime minister.
For these westernised Turks, acceptance by the EU represents a lifeline against the currents of Islamic populism Mr Erdogan represents. And they need encouragement, for Mr Erdogan's Islamists may be democratic, but the secularists, on the whole, are more liberal.
But the old privileged elite is not the only group in Turkey that stands to gain from being part of Europe. Minorities do well in empires, especially benevolent empires. Like the Catalans or the Scots, the Kurds in Turkey are in favour of EU membership because it offers a refuge from their own country's majority.
The sheer size of Turkey, and its population, worries Europeans, with some reason. But this fear is probably exaggerated. Now the Turkish economy is thriving, there will be less reason for poor Turks to seek work in other countries, let alone "swamp" them. And if the EU's hugely expanded membership were to stand in the way of a future federal state, this might not be such a bad thing. In any case, the addition of Turkey would hardly make the crucial difference.
From the perspective of the western-minded Turks, the pride of European membership is perhaps less important than the pain of rejection. But the same goes for the Europeans. If the most westernised, most modern, most democratic republic in the Islamic world were to be soured by anti-European resentment, this could not be a good outcome for the West - or, indeed, for the rest of the world.
Turkey is in a good position to guide other Muslim countries in a more liberal-democratic direction. Moreover, with a real prospect of joining Europe, Turkey would be better placed to defuse actual and potential tensions between Europe and the Middle East. Without Turkey, EU involvement in the Middle East still looks like Western imperialism.
The prospect of EU membership for Turkey would also dispel the outdated notion that Europe stands for Christendom. Christian religions certainly helped to shape European civilisation. But not all European citizens are practising Christians. Many are not Christians at all.
If a large democracy, with a majority Muslim population, can join the EU, it will also be easier to accept French, British, Dutch or German Muslims as fellow Europeans. Those who believe that common interests and liberal institutions should define the EU would gain by this acceptance. Those who seek a European identity based on culture and faith will resist it.
Alas, at this time of economic crisis, growing nationalism and inward-looking populism, the chances of a Muslim country becoming a member of the EU are slim, to say the least. Such a process cannot be forced on people. To insist on it, against the wishes of most European citizens, would smack of precisely the kind of undemocratic paternalism that has already turned many Europeans against the EU.
But the majority is not always right. And times might change. Then again, we might live to regret that times did not change fast enough.
Ian Buruma is a professor of democracy and human rights at Bard College in New York and the author of Taming the Gods: Religion and Democracy on Three Continents
* Project Syndicate