None of his disciples thought it worth writing anything down either. It was only when it became painfully obvious that Jesus' prediction of the end of the world in their lifetime wasn't going to happen that his followers finally realised that it might be a good idea to write his teachings down before all those who'd heard them were dead.
That is one theory.
My view is that in all probability the man never existed, at least as a historical person. In that case why we have none of his writings is obvious.
The main reason I think this is that the earliest Christian writings we have are the "genuine" Pauline epistles, and they seem to know nothing of a historical Jesus. Paul's Jesus did live on earth and was betrayed and resurrected, and so on, but in mythical time, not early in the first century. Paul knows nothing about the biographical details we get in the Gospels, even though in many cases we would think he would have referred to them.
We see Paul in the mid-first century leading and dealing with what seem to be well-established "Christian" churches all over the Greek diaspora -- especially Asia Minor. This is hardly twenty years after Jesus' supposed death, and well before any reported missions to them.
It seems more likely that what you have first is the rise of a Jesus-sacrificed-resurrected cult based on OT prophesies and after a number of other similar models active in the ancient world. This is not an earthly Jesus (except in mythical time) but a Jesus of the Heavens, about to return in glory (most new cults start off thinking they are in the end-time).
We need to resist the temptation of thinking that Christianity necessarily started just after the time of Jesus' death as told in the Gospels. It could well have been percolating a century or so even before Paul.
The stories of Jesus on Earth seem to have had two fairly independent origins -- the "Q" that preceded the synoptics, and another that led to (or was) the gospel attributed to John. The book that became Acts was probably written by the same person who wrote Luke, although from either lost material or
de novo. He clearly knew of Paul, and may have drawn some things from Paul's earlier writings, but the figure in his narrative has little connection with the historical Paul. At any rate, whether or not these were percolating during Paul's time is hard to tell, but seemingly outside Paul's knowledge.
The evidence for this scenario is substantial. There is the absence of any knowledge of the Tetragrammaton in the NT, something inconceivable if the authors were Jews, but not if the authors were Greeks using the LXX, where the Tetragrammaton does not appear.
Also, there is the invention of the "city" of Nazareth, for which we have no mention in the Talmud, the OT, Josephus (who does a comprehensive listing of Galilean habitations) or any one else. (The place now known as Nazareth was founded by Constantine's mother in the fourth century). How could this happen? It appears to have been a misunderstanding of a passage in Isaiah mistaken as a name and place of origin (in the Greek pattern).
There are, of course, many other "errors" in the NT that reflect that the authors had no personal knowledge of the place, but only the sort of general knowledge I might have were I to write a narrative and place it in Afghanistan. One of the most egregious is the naive placement of herds of hogs in Palestine, something that would have generated riots.
Then of course we have the simple fact that it was all written in Greek, and reflects Greek modes of thinking (sometimes identified as neo-Platonic, although I doubt the authors were that educated). An awful lot of Christian ink has been spilled trying, not persuasively, to explain how fishermen from Galilee came to write these things in Greek.
