Produce a Sura like it challenge
The Qur'an claims it is unique and challenges anyone to produce a Sura (chapter) like it:
"And if ye are in doubt as to what We have revealed from time to time to Our servant, then produce a Sura like thereunto"
"Say, "If mankind and the jinn gathered in order to produce the like of this Qur'an, they could not produce the like of it, even if they were to each other assistants.""
- "Ever since the Quran was revealed, fourteen centuries ago, no one has been able to produce a single chapter like the chapters of the Quran in their beauty, eloquence, splendor, wise legislation, true information, true prophecy, and other perfect attributes. "
The argument is based on the "literary miracle" of the Qur'an, which in turn implies God exists. Muhammad did not work other miracles, so the supposed "miracle" of the Qur'an has been emphasised to compensate for this perceived shortcoming.
- My holy book contains a property that has no earthy explanation.
- God must have done it.
- Therefore God exists.
Argument from ignorance
The argument depends on subjective human judgement. This is not a particularly independent, objective or reliable basis for an argument.
- "how do you quantify such a challenge? [...] basically the challenge seems to be a popularity contest, or an opinion poll. "
- "If I am the judge, then I will say that these newly composed Quranic verses are better than the age old Quran. If an Islamist is the judge then, of course, these new verses are blasphemy and nothing but gutter works. So, how are we going to come to a decision? "
Since there is no clear standard to meet, it is all to easy for apologists to move to goalposts.
- "Depending upon the different opinions of many muslims, the exact meaning of "surah like it" varies greatly. Some say it has to be eloquent and stylish like Quran, some say the verses should match the exact grammatical rules of Quran, some say verses must have to be meaningful, others say verses should not sound like that of soothsayers or pre-islamic poetry etc. There are many other such conditions muslims insist on in order to make the challenge as hard as possible. "
Unstated assumption that the Qur'an is perfect
This argument only works with the prior assumption that the Qur'an is perfect. The argument is therefore begging the question regarding the special characteristics of the Qur'an.
- "The circularity goes like this: If you're an orthodox Muslim, you believe that the entire Qur'an is the very word of God, and is therefore inerrant. As an implication of this, he or she also believes that there is no other writing as eloquent as the Qur'an. Therefore, any attempt to "produce a Sura like this" must fail - thus verifying that the Qur'an is the very word of God and inerrant. "
Some critics of Islam attempt to meet the challenge directly by producing original texts, such as http://suralikeit.com/
One Thousand and One Nights, which was compiled in Arabic, is more widely recognised by authors as a piece of great literature. 
The Qur'an is not that good
- "[The Qur'an] is strikingly lacking in overall structure, frequently obscure and inconsequential in both language and content. "
- "From the literary point of view, the Koran has little merit. Declamation, repetition, puerility, a lack of logic and coherence strike the unprepared reader at every turn. It is humiliating to the human intellect to think that this mediocre literature has been the subject of innumerable commentaries, and that millions of men are still wasting time in absorbing it. "
"It is as toilsome reading as I ever undertook, a wearisome, confused jumble, crude, incondite. Nothing but a sense of duty could carry any European through the Koran."
- — Thomas Carlyle on George Sale’s translation
A perfect book would not have required abrogation of earlier verses.
Distinctiveness does not automatically imply a divine origin
The distinctiveness of the Qur'an does not automatically imply a divine origin.
Books are distinctive in their own way
The Qur'an is distinctive but so are all other books. Just calling this one special commits the Texas sharpshooter fallacy.
- "All books are unique. Each person is different and unique. You can’t find two people alike. No two finger prints are alike, no two voices are alike, no two minds are alike, etc. "
- Argument from scriptural codes
- Scientific foreknowledge in the Qur'an
- Million dollar paranormal challenge
- Argument from religious complexity