The key reason is the Ottoman empire and it's policies.
Prior to the Ottoman empire, the Suljuk Sultanate (Sultanate of Rum) put tremendous stress on education. The Ince Minare Madrasa (source at bottom) was one of 24 Colleges built in the Sultanate of Rums capital of Konya and well over 50 of such structures were built Anatolia. The Sultanate of Rum was directly responsible for the height of Islamic literacy and their literacy rates far exceeding medieval Europe and quite likely even the Chinese.
However the Sultanate of Rum collapsed in the face of the Mongol invasion, becoming vassals of the Mongol empire. From these ashes rose the Ottoman empire who put almost the exact opposite stress on literacy and education.
There are a few reasons here:
1) The Supression of the Oghuz. Early Ottoman history is a long and violent struggle with the Oghuz tribes. To keep them subdued, education and literacy was withheld (and likely part of the reason of the ban of the printing press).
2) Nature of the Ottoman empire. The empire was somewhat a conglomeration of a variety of peoples and languages...Greek, Lydian, Phrygian, Cilician all fit into this empire (IE you could be a subject of this empire without really speaking the tongue of the empire). Many of these peoples were nomadic and education/literacy was an expensive prospect for little gain. I have seen the proposal floated that the Ottoman empire was actually more literate than given credit for, but these people were literate in their mother tongue and not the Turkish language.
3) Scripting (though this point is somewhat debated) wasn't easy. To make proper use of 'Ottomanish/Turkish' script, one needed to learn 2 languages to really be effective (correction in progress). The Elite would learn both Arabic and Persian, allowing them to effectively make use of their scripting, however most subjects of the Ottoman empire would only speak their mother tongue.
Edit from comments:
sourcing on that can be found here https://en.wikipedia.org/wiki/Ottoman_Turkish_language "It borrows, in all aspects, extensively from Arabic and Persian, and it was written in the Ottoman Turkish alphabet. During the peak of Ottoman power, Persian and Arabic vocabulary accounted for up to 88% of its vocabulary, while words of Arabic origins heavily outnumbered native Turkish words". Apparently if you didn't speak Arabic and Persian, the Turkish written language was pretty much unintelligible and a good segment of the Ottoman empire used kaba Türkçe ("raw/vulgar Turkish")
4) No specific mission to educate youth. Somewhere in Christian Europe, the mandate to educate youth came about. Mosques and Imam's had no such explicit mission to educate youth in this manner. As an odd side note, education was usually around the Quoran (believed to hold the key to all knowledge, not simply Theological), which was written in Arabic and does not help that much with Turkish literacy.
5) No stress on Education by the Ottoman empire. https://en.wikipedia.org/wiki/%C5%9Eevket_S%C3%BCreyya_Aydemir wrote in a few of his books that educational facilities in the Ottoman empire were exceedingly rare. Erdine (a major city close to Istanbul) only had one middle school and one high school to serve the entire city, and this wasn't uncommon throughout the empire.
By the time the Ottoman empire began to address this lack of education, it was already the 18th century and the majority of the world had long surpassed the Islamic world.
Madrasa information from Google books: (https://books.google.ca/books?id=qGb4pyoseH4C&pg=PT363&lpg=PT363&dq=sultanate+of+rum+literacy&source=bl&ots=Uf7p9JhSZR&sig=p_r7Ocu-dqGZkR1H2u06pVlEhY4&hl=en&sa=X&ved=0ahUKEwjWqqLSx9_YAhVNaq0KHdz_CmAQ6AEIUTAK#v=onepage&q=sultanate%20of%20rum%20literacy&f=false)