Paulsen's purpose in writing "the secret" in the manner he does is to highlight its importance in Brian's life.  The fact that Brian's mom is involved in this affair with the man in the car represents "the secret."  It also highlights the fact that he was not supposed to know about it.  He and Terry were riding bikes when they came upon his mom and the man, hence "the secret."  Paulsen's writing it in this manner suggests a couple of thematic elements.  The first would be to show the effect of the divorce on Brian.  It has impacted him so profoundly that he cannot even bring himself to articulate it, only referring to it as "the secret."  Additionally, the challenges present with "the secret" help to show Brian forced to accept the physical challenges of survival in the wilderness as well as the emotional challenges of dealing with the reality of "the secret" and the divorce it prompted.  It is interesting to note that while Brian was able to conquer the wilderness and survive, upon his reentry into society, his parents could not overcome their own challenges and reunite for his sake.  They tried it, but ended up capitulating, as "the secret "reemerged when Brian's mom and the man in the car continue seeing one another.