"This substitution of primitivism which must be anarchic (in its non-political sense) for morality gave my father his charm. His charm blinded not only his parents but even every old farty schoolteacher to both his complete lack of social awareness and of education."
Abhor is re-telling Thivai the story of her childhood and she begins by talking about her father. Her father was raised spoiled, uneducated and with no moral values, he created a primitive bond with his own mother and this lead to his own primitivism, or rather anarchic behavior. The fact that he was spoiled by his mother made him egocentric, and the fact that he wasn't educated with moral and social values didn't hinder his intelligence, it rather contributed to his manipulative charm.
"...when my father was being punished, he knew he was really being praised for being unlike other humans."
The novel is filled with paradoxical phrases that evoke a deeper meaning and strike at the root of an issue. This is one of the many. Abhor is talking about how her father was raised and what made him into a twisted character and the fact that his anarchic-self equaled punishment with praising not only explains his behavior further in life but also proves that he has self-awareness and enjoys being unlike other people.
"As a form of memory, beauty is a representation of what's past, over with, dead; but since now present delight was equal to memory, beauty could not be named."
This is an interesting and rather true definition of what beauty really is. Beauty is memory; it is the most appreciated in memory once the present moment of beauty is gone. If past is only memory then true beauty can't be named, can't exist in the present. These sort of philosophical existential moments of the characters could be seen as a voice of the author; the author speaking to the reader.