Hey! I can only answer this for the Middle-East but I hope it is enlightening.
There were a number of factors that influenced the late adoption of the printing press in the Islamic Middle-East. I'm going to highlight three of these - cultural emphasis on calligraphy, emphasis on clear parentage, and a fear that printers may change religious texts. Although I listed them separately, in reality these three factors often overlap and blend together.
First I want to clear some misconceptions.
Printing is not incompatible with the Arabic script. Although the letters slightly vary in form depending on whether they start, are in the middle of, or end a word, there is nothing that stops Arabic from being printed. This is why, even though the printing press wasn't commonly employed in the Islamic world until the 19th century, Arabic printing presses had been used in Europe since the early 16th century. The first Qur'an was printed in 1537 in Venice, Italy and there was a large Arabic press that printed secular Arabic works in the Netherlands.
Nor was there some sort of Islamic bias against learning. The Islamic world produced advanced works on mathematics, astronomy, and medicine - especially prior to the European renaissance when the Islamic world often outpaced the Western world in scientific understanding - and had libraries with hundreds of thousands of manuscripts.
Having established those two facts, we can get into why the printing press did not cause the same revolution that it did in Europe.
Calligraphy was and remains a highly valued form of art in the Islamic world. Calligraphists took pride in their great skill in not only forming aesthetically pleasing letters, but also in providing elaborate illustrations and patterns to decorate important works, both religious and secular. Printing presses, especially early presses with their often crude lettering, could not hope to match the beauty of hand-written manuscripts. Nor could they match their accuracy.
A class of professional scribes and copyists - called warraqeen emerged from the 8th century. These warraqeen did not only reproduce works but also played a pivotal role in how accepted they were. Works were seen as authentic not only based upon what information they contained but also who that information was written by. James Redman links this to the Islamic idea of "definitive knowledge" or that "the perception of what could accurately be prescribed as truth, fact, or reality was dependent not upon abstract statements but rather who confirmed those accounts". The importance of chain of transmission can also be seen in other facets of the Islamic world, such as the isnad that records who passed down what hadith from the time of Muhammad onwards.
With printing, this chain of transmission was impossible to verify. Additionally, prints were difficult to check for their accuracy (and given the limited accuracy of many of the early European prints of the Qur'an, this fear may have been well founded). In Arabic, a single dot can change the sound of a letter, and thus the meaning of an entire word (for example, the letters "ra" (ر) and "za" (ز) were often confused in early Italian prints of the Qur'an.) Although printing gradually improved, even a few errors could fundamentally change the meaning of a text and put off Muslim scholars from accepting printing.
This fear of corruption in religious texts was one of the driving forces behind the Ottoman Sultan Bayezid II's 1485 ban on the use of printed books. As Muhsin Mahdi writes, one look at the early Qur'ans "must have made Muslim readers of the Koran think that only the Devil himself could have produced such an ugly and faulty version of their Holy Book".
The ban of Beyezid II was followed by a similar ban from Sultan Selim I in 1515. However, he allowed for dhimmis, or religious minorities such as Christians and Jews, to print books. This is why the first Arabic printing press in the Ottoman Empire did not open until 1720 under the reign of Sultan Ahmed III, when a Hungarian convert to Islam named Ibrahim Muteferrika was enlisted, even though the first Hebrew printing press in Constantinople opened at the end of the 15th century. Despite the spread of presses in Anatolia and the Levant, it took even longer for printing to become common in areas like Egypt, which only developed a printing tradition following Napoleon's 1798 invasion.
Finally, I should note for the sake of completeness that some believe the Arab world developed printing much earlier, even earlier than the Europeans. Geoffrey Roper writes that there are allusions to printing in poetry as far back as the 10th and 14th century in Fatimid Egypt. He adds that early mass produced charms and amulets, bearing prints of the various holy names of God, were found surviving back to the 10th century, with more from the 13th to 16th centuries. However, if it did exist then, it was not widespread and was therefore not the revolution that you were looking for.
So, in sum, it was largely cultural factors that limited the acceptance of the Printing Press in the Middle East until the 19th century. Due to heavy reliance on knowing the chain of transmission for works as well as the necessity for ensuring the accuracy of copies - something harder to do on a printing press - it merely took longer for the printing presses to catch on in the Arab world.
Sources
"Commencement of Printing in the Muslim World: A View of Impact on Ulama at Early Phase of Islamic Moderate Trends" by Moinuddin Aqeel.
"Printing History in the Arabic-Speaking World" from the Yale University Library
"From Pen to Press: Debates on the Development of Islamic Printing" by Samuel Taylor
"Muslim Printing Before Gutenberg* by Dr. Geoffrey Roper
It actually did have a revolutionary effect in China, similar to in Europe. This has been discussed a couple times here, I'll link this one by /u/FraudianSlip and /u/thanatos90. While the Chinese tended to use woodblock printing and the movable type, printed documents and books were widespread and available to an extent comparable to the Early Modern West. This had a similar impact on the wider culture, including things like vernacular literature and the spread of Buddhism (or more accurately, the form of Mahayana Buddhism that gained currency starting in the eighth century and radiating from Sichuan). Wing Tsit Chun's Buddhism in China and Mark Edward Lewis' China's Cosmopolitan Empire both discuss this.
I can't exactly give a historiography of how the narrative that printing was revolutionary in the West and solely in the West, and laid the basis for how the West is special, developed, but it isn't exactly unusual. There are all sorts of accepted narratives that gained wide currency among scholars of the modern West that were made essentially without reference to non Western sources and scholarship (for example "early globalization" in the Indian ocean, cf Asian merchants and businessmen in the Indian Ocean and the China Sea). Luckily this is changing, due to the post colonial reorientation of empire scholarship, and the rise of academics from outside the West, but it will take some time to fully unstick.