This is one of the most puzzling questions of the novel. McCandless apparently wanted to explore America on his own--without any interference from his parents. He also wanted no monetary assistance, thus the burning of what money he had and the earlier donation of the remainder of his college fund. He did not want his parents to locate him, because he probably knew that they would try to come for him. I don't believe McCandless' intent was to disappear forever, but only until his sojourn was complete. Some of his decisions were obviously unwise, but he must have planned to spend his travels in a strictly bare-bones manner.
First, his past identity and life troubled him. He had an estranged relationship with his father, and could see little point in living his life according to the formula others had given him. By the time he has the small ceremony and burns his license, social security card and money, he is firmly dedicated to this idea of being completely free.
In other words, this isn't a rash and spontaneous act on the part of Chris McCandless, it is the next logical step to someone who is both literally and figuratively stepping of into the wild. Rather than a troubling event, it seems as though he found it quite liberating.