What is the main conflict in The Fall by Albert Camus?

Clamence's profession as judge-penitent is made up of two, apparently conflicting, aspects, just as he says, humanity is doubled. This can be observed, for instance, in a tale Clamence tells of a Nazi soldier asking a mother, with every appearance of politeness, which of her two sons should be executed. The paradox of such courtesy overlaying such atrocity demonstrates the degree to how two apparently opposite human traits can manifest themselves at the same time.