You're right.  Chris McCandless is a difficult character to characterize.  McCandless is quite an ethereal character, always evading our grasp as readers.  He even speaks about himself in the third person which gives him an even bigger distance from us.  Still, two qualities that he definitely has are being determined and stubborn.

McCandless was also smart (or at least smart enough to go to college) and in his twenties.  He always had a certain hatred for his parents, however, who were quite strict and treated him poorly. 

McCandless wants to "find himself" and, more importantly, discover the truth of mankind which almost leads to his survival in the wilderness.  My very favorite quotation about McCandless' stubbornness can be found on our eNotes pages:

Nevertheless, his insistence on doing things his way caused him to neglect several basic precautions that would probably have kept an experienced woodsman alive: a good hunting gun with ample ammunition, reliable information about the area he would be venturing into, and a dependable U.S. Geological Survey topographic map.

This pride, determination, and stubbornness is his own downfall.  McCandless failed to get accurate info about the area, get a good gun, and obtain a good map.  This reminds me a lot of the man in "To Build a Fire." 

McCandless might first be defined by his non-conformism and his willingness to eschew the financially comfortable background in which he was brought up. Krakauer states that he 'believed that wealth was shameful, corrupting and inherently evil'.  This non-conformism is perhaps defined by his willingness to ally himself to the civil disobedience of some of the transcendentalist writers, Henry David Thoreau being the prime example. This was not to say that he was not, at times, pragmatic and viewed money earned by what he believed to be moral and honest labour to be valuable. While he gave up his inherited wealth  and 'donated the balance of his bank account to OXFAM', he was nonetheless willing to work for Wayne Westerberg and at McDonalds for money when he needed it. He seems to have drawn the distinction at having too much money and acquiring it as a result of unearned privilege. 

Krakauer, however, is clear to state that he was no liberal, stating that he 'was a vocal admirer of Ronald Regan' and cited Thoreau about the evil of governance - one might describe him better as a libertarian than a liberal. He was, however, it would appear, morally driven, perhaps in part due to the extremity of his reaction to his parents' troubles and his judgement that his father was a 'sanctimonious hypocrite', particularly in relation to the latter's concealed divorce. McCandless's moral motivation, however, found more constructive means than in simply moralising. He was a fan of direct action, Krakauer recounting a number of incidents from his school days where he would practice personal philanthropy such as he would 'wander the seedier quarters of Washington, chatting with prostitutes and homeless people, buying them meals'. It appears that he believed less in state intervention and more in personal responsibility for the poor. One might also claim that he saw an inherent nobility in poverty and liberty, embodied in the name that he chose for himself, 'Alexander Supertramp'. 

The quest for personal liberty is clearly embodied in the willingness to give up his old identity, not only his financial worth and connection to his family but, moreover, his very name. Other examples, of course, come with his desire to live entirely alone and by nature in Alaska but are pre-figured by his quest to kayak down the Colorado river, defying park laws that meant he had to have a license. 

Whether we would characterise McCandless as hubristic (i.e. with over-arching pride that led to his own downfall) or not is an interesting question. I've linked below to an interesting enotes.com essay on this point and the question of whether he is a tragic hero or not.