"You must understand this. We own nothing except ourselves. This world and its laws, allows us nothing except ourselves."
Notes from Wikiquote
What Styles seems to be implying is that individuals can only really claim themselves but, everything else is a possession that can be taken away. His remarks that "this world and its laws" allow for nothing else, simply imply that a person's identity is the only thing that cannot be taken away under the oppressive rules of the South African government.