This objection has been made popular by scholars such as Bart Ehrman, who has written:
"Jesus' own followers...were mainly lower-class peasants--fishermen and artisans, for example--and...they spoke Aramaic rather than Greek. If they did have any kind of facility in Greek, it would have been simply for rough communication at best (kind of like when I bungle my way through Germany, to the general consternation of native speakers). Even more strikingly, the two leaders among Jesus' followers, Peter and John, are explicitly said in the New Testament to be "illiterate." [Acts 4:13]...In the end, it seems unlikely that the uneducated, lower-class, illiterate disciples of Jesus played the decisive role in the literary compositions that have come down through history under their names." 
However, as New Testament Scholar Timothy Paul Jones reports, Dr. Ehrman only gives us part of the picture:
"...he [Ehrman] is correct that some members of the Judean ruling council pointed out that Peter and John were agrammotoi or "unschooled" (Acts 4:13). How, then, could such testimony-stories that may have circulated first in coarse Aramaic- have turned into Greek documents found in the New Testament Gospels today?
The first difficulty with Ehrman's interpretation is that the word agrammatos does not necessarily imply that Peter and John were illiterate. In the context of the Jewish council, agrammatos likely meant "untrained in the Jewish law." If this is the case, the council members were pointing out that, despite their boldness in interpreting the Hebrew Scriptures, Peter and John had not been schooled as rabbis." 
Were the traditional authors of the four NT gospels "illiterate" as many claim? Jones provides an in-depth look in hopes of answering that very question.
Matthew the Tax Collector
"In the book that bears his name, Matthew is presented as a "publican" or "tax collector." It is doubtful that any early Christian would have fabricated this bit of vocational trivia. After all, the very idea that Jesus asked a tax collector to follow him must have been a bit embarrassing. When the Gospels were written, Roman governors expected tax collectors to stockpile personal wealth by cheating people- and most tax collectors apparently complied with this expectation. Not surprisingly, tax collectors rarely make it to the top of anyone's list of most-loved citizens.
In Roman rhetoric, to refer to someone as a tax collector was to call that person's honor into question. In the writings of Josephus, the Jewish historian told how a Judean tax collector bribed the corrupt governor Florus not long before Florus incited the Jewish rebellion against Rome. And, according to the Gospels, folk in Judea and Galilee grouped tax collectors with drunkards, gluttons, pagans and adulterers (Matt. 11:19; 18:17; Luke 18:11). Simply put, answering the classified ad that read "Become a Roman tax collector! Make millions fleecing your friends!" was not the most promising pathway to personal popularity in the ancient world.
But there was one skill that tax collectors did possess. They could read and write.
Tax collectors were, in fact, know to carry pinakes, hinged wooden tablets with a think wax coating on each panel. Tax collectors used styluses of metal or bone to etch notes in the wax- notes that, in most cases, were later translated and rewritten on papyrus. Papyri from Egypt prove that tax collectors also wrote receipts and registers for citizens in their villages.
Despite Ehrman's disdainful description of the first disciples as "uneducated, lower-class, illiterate," a tax collector such as Matthew could not have fit such a description. The daily tasks of a Galilean tax collector required him to collect, copy and record information, probably in multiple languages." 
Jones continues by describing the skills that a physician in the ancient world would have most likely possessed:
"...a physician would seem to have possessed, at the very least, the capacity to read the summaries of medical knowledge that flourished in the first century. What's more, papyri from Egypt prove that ancient physicians and their scribes frequently wrote reports for law-enforcement officials regarding suspicious injuries and possible causes of death, as well as statements for slave masters certifying the health of slaves. So- if indeed Luke was a physician, as the letter to the Colossians suggests-it's unlikely that he was "illiterate" or "uneducated." And many physicians were capable of pulling together various eyewitness accounts into a coherent report, just as the preface of Luke's Gospel implies that the author has done." 
Mark and John
"That leaves Mark and John. When it comes to these two witnesses, Ehrman may be correct: Though it is by no means certain, either or both of these men may have been illiterate. Yet even this doesn't preclude the possibility that eyewitness sources stand behind the NT Gospels.
In the first century A.D., professional scribes were readily available to render messages from other languages, including Aramaic, into polished Greek. Complex legal titles, eloquent epistles to family members and simple commercial receipts all required secretarial skills- and provided livelihoods for a multitude of scribes not only in urban areas such as Ephesus and Rome but also in Galilee and Judea. And prosperous patrons weren't the only people that used professional scribes; persons from poorer classes employed scribes too. Even though Paul was completely capable of writing Greek (Galatians 6:11; Philemon 1:19-21), scribes penned Paul's letters for him (Romans 16:22; see also 1 Peter 5:12).
It's entirely possible that Mark and John employed professional scribes to render their oral accounts of Jesus' life into the Greek documents that centuries of copyists have passed down to us. If so, they would still have been the sources of these Gospels, even if they didn't pen the actual words.
I do find it intriguing that the simplest Greek in the New Testament is found in the Gospel According to John and the Gospel According to Mark, the two Gospels whose traditional authors might have been less than literate. In fact-after translating hundreds of Greek epigraphs, papyri and writings from prominent second-and-third-century Christians-I still haven't found a document written as simply as the Gospel According to John." 
So, it seems, as is often the case with Professor Ehrman, there is indeed more to the story! Ironically, even Ehrman himself admits that the New Testament is reliable! Check it out here.
For those desiring to explore the authorship of the Gospels, go here or here.
Courage and Godspeed,
1. As quoted by Timothy Luke Jones in Misquoting Truth, p. 113.
2. Timothy Luke Jones, Misquoting Truth, 113-114.
3. Ibid., p. 115.
4. Ibid., p. 117.
5. Ibid., p. 117-118.