The title of Trevor Noah's Born a Crime is critical to understanding how race had an impact on the understanding of himself. He's alive only because his parents both technically committed a crime. Under apartheid in South Africa, relations between people of different races were illegal. With his mother being black and his father being white, Noah's birth was evidence of a crime committed by his parents.
The laws in South Africa during the early years of his life also made it impossible for him to be around both of his parents in public at the same time. That caused Noah to become distant from his father from an early age.
At the same time, because he was half white, he had rights and privileges in South Africa that his mother and maternal relatives did not, because they were black.
On the topic, he writes,
When I look back I realize she raised me like a white kid—not white culturally, but in the sense of believing that the world was my oyster, that I should speak up for myself, that my ideas and thoughts and decisions mattered.
However, he was not privy to the same rights as white people such as his father because he was only half white. In that sense, Noah didn't fit into either side of his family and was a societal outcast in South Africa, which had a class structure set up for white people and black people but did not account for people of mixed race because it was technically a crime for someone like him to exist.