Why didn't Jesus write a book?

Moses wrote books, Muhammad had his followers write a book while he was still alive, but Jesus didn't write anything down or ask his disciples to transcribe any of his teachings. The gospels warn us to be wary of false teachings, but if they were written so long after Jesus' death, how can we be sure that they are not false teachings? Even the proof that they offer to test against false teachings (that it will be in the fruit that they bear, whether it comes to p as true or not) seems doubtful since it has been about 2000 years since Jesus lived and we haven't seen his return. How can we trust these books as true and not merely sincere, but wrong, since Jesus never bothered to write anything down himself?