One way of answering this question would be to look at the letter that Chris writes to Ron Franz, the man who was so impressed and taken with Chris that he even offered to adopt him. Note what Chris suggests Ron does with his life:
I'd like to repeat the advice I gave you before, in that I really think you should make a radical change in your lifestyle and begin to boldly do things which you previously may never have though of doing, or been too hesitant to attempt. So many people live within unhappy circumstances and yet will not take the initiative to change their situation because they are conditioned to a life of security, conformity, and conservatism, all of which may appear to give one peace of mind, but in reality nothing is more damaging to the adventurous spirit within a man than a secure future.
The advice Chris offers is very similar to Thoreau of Emerson's view of the world, which rejects capitalist society and its slavish adherence to jobs that take over people's lives and grind them into the ground and encourages them to be free from such restraints to live their own lives. Chris embodied this in his own life, only working when he had to in order to earn money for the next stage of his journey and moving around as he pleased, without any cares or responsibilities. He, although he was very well educated and clearly very intelligent, did not do what was expected of him by his parents: he did not get a job, buy a house, get a new car. Remember how he reacted when his parents tried to buy him a new car. Chris's whole life was spent trying to find a different way of living compared to the way that the majority live.
Into the Wild is the story of a well-to-do young man who gives up his worldly possessions to carry out an adventure living in nature. In many respects, it has elements of books like Thoreau's Walden, although Chris McCandless (unlike Thoreau) dies in the end.
How does McCandless reject society? American society seems to center around the idea of the American dream -- of going to college to get a good job, to buy a house, to buy a car, etc. McCandless fared well at Emory, a top university, and seemed well on his way to achieving that dream. However, he seemed troubled by the materialism with which he was raised and the problems that wealth and the acquisition of wealth caused in his own family.
In the end, he did what few others in his position would do. He "rejected society" by giving away what our society puts a strong emphasis on -- possessions. He gives his money (roughly $25,000) to charity and even burns the money in his wallet. In this way, he rejects the societal values of property and the American dream in pursuit of a higher ideal in nature.
Hope this helps!