The big symbolic step that Chris McCandless undertakes when he leaves is to give away all of his savings to OXFAM. This is combined with the step of avoiding contact with his parents and sister in any way. Note how this is reported in the text:
Shortly thereafter; he donated the balance of his bank account to OXFAM, loaded up his car, and vanished from their lives. From then on he scrupulously avoided contacting either his parents or Carine, the sister for whom he purportedly cared immensely.
The symbolism of this change is of course very important. Chris, having gone through difficult stages in his relationship with his parents where he resented their interference, and the way that they (according to him) tried to control and manipulate him through their wealth, is giving away all the savings that they had given him in one dramatic gesture. For a young man who was obsessed with the writings of Emerson, it is easy to see this step as being symbolic of his own attempt to be independent and self-sufficient, and to walk to a "different drum" in his rejection of society. This is likewise supported by his decision to not contact any family member. For Chris, trying to live the kind of life that was characterised by self-reliance and being by himself in nature, he could not afford to have any emotional attachments that would hamper him or prevent him from achieving his goal, no matter how hard those attachments may have been to break. However, it is after this that Chris refuses to allow any relationships with anybody to develop into something that could tempt him to settle down and sacrifice his life of restless wandering.