Why did Brian's mother give him a hatchet?

In chapter 1, Brian is flying on a small bush plane to stay with his father, who is a mechanical engineer working in the oil fields of Canada. Brian's parents recently divorced, and his father has custody of him throughout the summer. When Brian opens his satchel on the plane, he pulls out a hatchet with a rubber handgrip. Brian then remembers when he received the gift from his mother before he left to stay with his father in Canada. She had given Brian the hatchet as a gift so that he could use it while out in the woods with his father. Initially, Brian felt like the gift was useless, but he eventually learns that it will be essential to his survival following the plane crash. Fortunately, Brian survives the crash and learns to use his hatchet for a myriad of purposes. Throughout the novel, Brian becomes an expert woodsman and survives alone in the expansive, challenging Canadian wilderness.

Brian's mother gives him a hatchet because she thinks he might be able to use it while out in the woods with his father.  
When the story begins, Brian is on his way to Canada, where his father now lives. His mother and father recently went through a divorce, and the courts set up a system that has Brian living with his mom during the school year and with his dad during the summer. Dad now lives in a remote, wooded area. Brian's mom buys Brian the hatchet as a going-away present. She tells Brian he might be able to use it while out with his dad in the woods.

Brian took the sack and opened the top. Inside there was a hatchet, the kind with a steel handle and a rubber handgrip. The head was in a stout leather case that had a brass-riveted belt loop.
"It goes on your belt." His mother spoke now without looking at him. There were some farm trucks on the road now and she had to weave through them and watch traffic. "The man at the store said you could use it. You know. In the woods with your father."

Unfortunately for Brian, the plane crashes, and he never makes it to his father's place. Fortunately for Brian, he has the hatchet.