That's what Brian wants to know, too, in Chapter 16 when he feels that the moose has attacked him for no reason at all. It's senseless, he thinks, and insane for the moose to have charged him:
So insane, he thought, letting sleep cover the pain in his chest—such an insane attack for no reason and he fell asleep with his mind trying to make the moose have reason.
Long after this incident, Brian continues to think of the moose attack as something crazy, something that could not be explained rationally by finding a cause for it. Even after he gets home and is able to research the things he didn't know during his time in the wilderness, like the real name ("grouse") of the creatures he'd called "foolbirds," he still doesn't know why the moose had attacked him.
Brian does accept, however, that nature's power is sometimes random and cruel. That's what he learned from the moose attack as well as the tornado that hit his shelter while he was still recovering from the damage the animal had inflicted on him.
Still, as readers, we're curious to understand why the moose did attack. Surely it wasn't just for fun, and surely the enormous moose didn't feel threatened by Brian's small arrow that he was using to find food at the time, right? The novel provides no answers. But if you Google why female moose like the one in the story do attack, you'll learn that they are extremely protective of their calves. If the moose in the story had her calf nearby, she might have attacked Brian even though he didn't provoke her. (Her intention may have been to demonstrate to Brian that he'd better not even think about getting close to the moose calf!) In fact, because female moose are known for being so protective and defensive, this discussion from SurvivalGrounds.com indicates that in Canada, female moose are responsible for more human deaths than even the grizzly bear.