Why did Bruno’s parents not want Bruno to find out about his father being the commandant of the Nazi camp?

There are two basic reasons that Bruno’s parents try to keep from him the fact that his father has been appointed the commandant of Auschwitz. One reason is to protect his innocence as a child, part of which is his high opinion of his father. This reason completely backfires, though. An early indication that his lack of knowledge will have bad consequences comes when Bruno tells Father that his appointment is a demotion because they have been moved to such an awful place. Additionally, beyond not wanting Bruno to know that Father is responsible for the killings, his parents simply do not want him to know that people are getting killed. The full impact of withholding this information is Bruno’s death in the camp because he did not understand its purpose.
Another reason to keep Bruno in the dark is to maintain secrecy. In the first few years that the camps operated, the Nazis tried to keep their functions secret. This was largely possible because so few people were released or escaped. The people who might be rounded up and sent there thought they were labor camps, not death camps.