I think that there are many reasons that could be used to explain his main fear, as the subtext of the question indicates. I think that White society does seem to be Bigger's predominant fear. There is a fear of what White society thinks of him when he cannot say anything to Mary's mother about him being in the room. His fleeing from White society's police and the relationship and perception he has about White society all result in his fears of it. His fears are certainly justified and well grounded in what is the reality for someone in Bigger's condition. Yet, they are fears and Wright might be using this to explore how African- Americans, particularly African- American males, perceive White society. The odd element in this configuration is that Bigger does believe in the American Dream. The belief that Bigger can actually find his own niche in the American Dream is one that inspires him to get the job that enables him to be near Mary in the first place. The fear of White society is enhanced by his desire to be close or to be a part of it. In this light, one can see his fear as a twisted condition of reality within it.