Says who? Many Muslim states have embraced enlightenment ideals. For Indonesia to Senegal, there are many thriving democracies in Muslim-majority countries. In the late 19th and early 20th centuries, Iran and the Ottoman Empire were clearly in line with Central and Eastern Europe. The successful constitutional revolutions in Iran and the Ottoman Empire pre-date Russia's, for example. Does Russia now have more claim to the enlightenment than Turkey and Iran? While many Muslim-majority countries have not embraced the Enlightenment (Saudia Arabia doesn't even have a constitution--if you can't tell, Rousseau is probably my favorite Enlightenment thinker), some Christian-majority countries (particularly in Africa) haven't embraced all of what today would be called "enlightenment values" more than some Muslim-majority countries.

It's generally hard to ask why something didn't happen. It's much easier to explain why something did happen. The Enlightenment was a unique moment in history, with many important necessary conditions (printing presses, political division, polyglottism, sponsorship, universities, etc etc). Many important things generally seem to have been invented once, and then diffused. Capitalism seems to have only developed once. Moveable type printing presses. Modern nationalism. Most people believe even the wheel and axel was only invented once (though it existed in toys among the pre-contact Incas, it was never put to productive use). While some things developed seemingly independently multiple times--writing and agriculture are the biggest two--very many things seem to have only occurred once and spread from there. Why did the Christian world not invent zero, or rational numerals? Why did the Christian world invent geometry, but not algebra?

For more, you might be interested in a recent piece in the Guardian: Stop Calling for a Muslim Enlightenment by Christopher de Bellaigue (he's not an academic, but he's a public intelletual who regularly publishes in either the New York Review of Books or the London Review of Books and is quite good).

Do you have anything to support your premise? Would modernist movement such as the young turks not at least suggest that your premise has problems?

First of all, the notion of an 'Islamic' society is a very recent one, and not at all supported by the realities of life in the Middle East before the 19th century. Edward Said's Orientalism talks a lot about the fallacy of lumping that entire section of the world under the label of one religion for many reasons, the largest being that the idea of an Islamic political identity is a very modern invention that is a function of both the anti-imperialist sentiments that arose in the 1800s and the Hamidian desire to create a sense of Ottoman nationalism.

By 1900, the elite of the Ottoman Empire were very westernized. Ottoman literature in the era was mostly in the tradition of Zola and other realists. Materialism was in vogue. The Young Turk constitutional revolution, which was supported by these elites, was secular and informed by ideas from the French and American revolutions.

So 'Enlightenment' ideas have definitely perfused through the middle east. It's an unfortunate consequence of history, and part of the lingering effects of imperialism, that sectarianism is so present and religions identities so intertwined with politics.