Why didn't the Buddha write a book outlining his teaching?

Perhaps with the exception of Laozi, most sages, founders of religion, & great thinkers from virtuous tradition do not leave us books authored directly by them. In most cases what we have is books written by their followers or commentators. Some did say why they don't want to write. Did the Buddha say why he prefers oral transmission? --- Thank you for the responses and historical references, it's hard to believe that the cause for not writing a book to be lack of written script or writing material, India wasn't that lacking, they even had some intriguing advanced mathematics compare to other civilization and writing did exist by the end of the Vedic period which aligns with Buddha time... But perhaps, as @Andrei noted the oral tradition was more advanced and the preferred method. I asked because I thought maybe the Buddha, the same as other thinkers, saw writing as an incorrect way to transmit his message. For example, Socrates compared writing to dead painting as quoted below, but his view is not directly applicable to Buddhism and in a wider sense to Vedic oral transmission, because the method (i.e the oral transmission) is not about dialectic rather repeating the exact word and phrase. So, for an external observer is an excellent candidate for writing. > The painter’s products stand before us as though they were alive. But > if you question them, they maintain a most majestic silence. It is the > same with written words. They seem to talk to you as though they were > intelligent, but if you ask them anything about what they say from a > desire to be instructed they go on telling just the same thing forever .