Transcendence and enlightenment
Henry's journey mirrors a famous novel by Herman Hesse called, Siddhartha, which tells one version of the Buddha's story. Both Siddhartha Gautama and Henry are spoiled sons of powerful men who tried explicitly to insulate them from suffering. Then, when Henry's brother dies, he is forced (like the Buddha was) to face trauma, tragedy, and suffering directly. At his brother's behest, he makes the journey up a mountain, a common literary metaphor for transcendence.
Henry's enlightenment is complete when he realizes that his father's attempt at "the good life" was misguided, because his father lives in a paranoid state about bad things that could happen. Henry feels that he will be more emotionally and ethically successful facing the tragedy of life head-on, instead of avoiding suffering.
Human failure and forgiveness
Henry must forgive the inadvertent murderer of his brother. He is on the journey with the man before he ever learns the truth about Chay's role in Franklin's death, but after he learns more about Chay's life, he realizes that if he can put the accident into perspective, he can start to empathize with Chay. This also happens again when Louisa reveals that Franklin himself needs to be forgiven for the various aspects of his character that were corrupted by his spoiled upbringing.
Suffering and avoidance
Henry's dad decides to give his son the best life possible, but instead of considering Henry's moral enlightenment, he simply spoils his family with his extravagant wealth. Later we find that this treatment made Franklin into a closet racist, but when Franklin dies, the family is not allowed to continue on in their blissful ignorance. Henry is forced to confront the truth about life and suffering, and he concludes that his father's attempt to prevent tragedy is misguided. Instead, he will learn to lean in and learn whatever tragedy tries to teach him.