The climax of The Sign of the Beaver occurs when Matt must make the choice of whether to stay at his family's cabin and wait for them to return or to join Attean's tribe and travel to a less populated area.
This choice is an extremely difficult one for Matt to make. Throughout the story, we see how Attean's family takes Matt in, treating him as their equal, and Matt learns to trust them with his life. Attean and Matt become as close as brothers, and though the Native American tribe feels some animosity towards white people in general, they are all friendly with and welcoming to Matt. The affection that has grown in his heart for them and their way of life makes the opportunity to go with them and be a permanent part of their tribe very appealing to Matt; yet, he decides not to go. Charged with keeping his father's cabin safe until his family's return, Matt does not walk away from his responsibilities. This decision is even more impressive when we consider how Matt is at this point not even totally sure his family will ever come back at all, as they are long overdue and he has no means of communicating with them. Still, he stays. His loyalty to them and his sense of personal responsibility mark his newfound maturity.
At its core, The Sign of the Beaver is a coming of age story, and Matt's ultimate choice not to abandon his family, though that means giving up a life he may have preferred, shows that he is leaving behind his carefree boyhood and becoming a man who must and does make the right choices, even if they are difficult for him.