Chris had a troubled and very angry relationship with his father. This relationship--or Chris's rejection of it-- was centrally important to motivating Chris's behavior in the few years he had between graduating from college and dying in Alaska.
Chris forcefully rejected his father's materialism, telling his sister that he didn't want to be "bought." In response to what he believed were his father's attempts to smooth over difficulties with money, Chris rejected money. He gave an inheritance he received to Oxfam, then later abandoned his car and burned his cash. He deliberately lived on the margins of society, working at different times at a ranch or at a MacDonald's. When he hit the road after college, he was so determined to be out from under his father's control that he didn't let anyone in his family know his whereabouts. This, as we know, had fatal consequences: when Chris got into serious trouble, nobody knew where or how to find him.
Chris also despised his father for having a second family that Chris knew nothing about growing up, leading him to believe his whole childhood had been a sham. Chris's determination to be different from his father drove him to read authors who advocated a simple life, such as Tolstoy and Thoreau, to live alone for long periods and to pursue his counter-cultural path.
Considering the above post, making "truth" the focus of your essay would be a good way to go. Use the essay to develop the many ways that Chris did not have "truth" at home - the double life, the materialism, the "phony" socialite life - and then compare those things to the "truths" he is looking for in the world and in wilderness.
Chris McCandless' relationship with his father was strained at best. Chris was an opinionated, determined, and stubborn young man with high ideals and little room for compromise. His father is a hardworking man with high standards who shared his son's inabilty to compromise. Chris was always critical of his parents and their lifestyle, but that criticsm turned to outright anger when Chris learned that his father had lived a double life with another family for a time. Chris saw his father as a liar and a hypocrit and he was never able to forgive his father. A recurrent theme in Chris' journal was a search for "truth", and he linked that search to the lack of truth he perceived in his family life. After graduating from college Chris felt the need to flee from his family and their expectations in order to seek the truth that he felt he had never experienced.