I suppose one could argue that the conflict is between Chris McCandless and his family or society at large, as he was estranged from his family and very disillusioned with society in general but, to me, the central conflict is actually between McCandless and nature.
Inspired by the likes of writer Jack London, McCandless burned his remaining money, his driver's license, and abandoned his car to venture north towards Alaska, supposedly to live out his dream of getting back to the land. He goes there alone, and wanders off (woefully unprepared) into the Alaskan wilderness before the onset of a typical winter there.
The resolution of this central conflict is that nature humbles McCandless. It corrects his arrogance, and in the end, kills him.
The previous educator makes a very good assessment regarding McCandless's arrogance which, unfortunately, leads to him starving to death. His death by starvation is also a cruel irony, for he abandoned his life of upper-middle class privilege due to his sense of there being something essential that was missing from that life. One could argue, then, that another conflict in McCandless's story is between who we really are and the roles that we are expected to play based on aspects of our identity, such as race, gender, or class.
At various points in the book, and in the film based on the book, McCandless's alienation from society is emphasized. He knows that society expects him to take comfort in material things—the physical evidence of success and privilege—but he does not. This is another explanation for burning his money and abandoning the vehicle his parents gave him.
While it is certainly possible to live without a car, McCandless was less prepared than he thought he was to endure life without access to certain necessities, such as money to buy food. He believed that he could live off of nature's resources, as a wild animal would, though he had not been prepared for such a life. He dies as a result of being unable to escape the background that he eschews. He is a product of society and all of its comforts and discontents. He was woefully and tragically unprepared for life in the wild.