Why does Balducci think that Daru has "always been a little cracked?" Why does Balducci give Daru freedom of choice?
Besides utilizing the helpful characterizations provided at the eNotes summary, you might begin by examining the context, or setting.
Leading up to this conversation, Balducci speaks of "wartime" and how "things are brewing." In short, there is French-Arab conflict, and Daru and Balducci are the minority of French citizens who are either teaching or policing the area. Daru is expected to switch from his role as educator to role as soldier/officer due to it being "wartime."
What choices does Daru make that Balducci questions, making Balducci call him "cracked"?
- Daru not restraining the Arab's hands with rope (which is how Balducci brought him to the schoolhouse); and
- Daru keeping his shotgun in his trunk rather than by his bed.
While Balducci seems amused as he says this, even fond for the remembrances of his son that Daru inspires, he still wants to lend Daru his revolver.
Why does Balducci give Daru a choice? You can argue different interpretations on this one. Examine closely the conversation where Balducci insists that Daru at least sign the paperwork showing that the prisoner has been delivered. What does Balducci say about Daru's character?
"I know you'll tell the truth. You're from hereabouts and you are a man."
Does that imply that Balducci has a) a prior relationship with Daru and b) a trust of "locals" and c) a trust of Daru's character? Perhaps so.
What also is Balducci most concerned with? The bureaucratic element, or signing of the paperwork. What does that show about Balducci's character and perhaps explain his decision to let Daru make his choice?
Balducci is armed and could turn his revolved on Daru, yet he doesn't. How might that explain both his character and his decision not to force Daru into action?
Finally, back to the setting. How might the setting explain why Balducci doesn't insist on Daru turning in the prisoner?