Why does John's father want to keep secret what John has learned about the Place of Gods in By the Waters of Babylon?
The answer to this question is linked implicitly with one of the central quotes of the play: "Perhaps, in the old days, they ate knowledge too fast." Note too the metaphor that John's father uses to describe truth:
Truth is a hard deer to hunt. If you eat too much truth at once, you may die of the truth. It was not idly that our fathers forbade the Dead Places.
It is clear that John and his father are not concealing truth as part of a despotic control of power - they are concealing truth as a measure to protect and help their people. Though clearly, the last paragraph of the story, which states John's plans to return to the city and discover more and to "build again", indicates that this truth that John has discovered will be revealed bit by bit when his people are ready for it.
I guess when you have a culture that has been built around central "truths" for so long, to challenge those truths and expose them as lies would have a massive impact on the people in that culture. Better, therefore, to slowly bring in a different way of thinking rather than force everyone to experience the dramatic, life-changing epiphany that John experiences in this story.