Okay so in chapter 4 of hatchet, Brian is so troubled by his parents' divorce that after crashing the plane and him being able to think again, he thinks about the Secret. Brian has kept this Secret for awhile now. He thinks it's the reason that his parents divorced.
I think it was because of the pressure he felt from the natives watching him. He felt as though he should shoot it to show his strength and that as a white man he was unafraid and superior.