In The Stranger, why does society need Meursault to have felt grief at his mother’s death?
The Prosecutor is trying to show that Meursault is an unfeeling, nihilistic person with criminal tendencies. Because Meursault is so indifferent to the rules of society, the Prosecutor has a relatively easy time in doing so. Meursault's "society" would be more understanding if Meursault behaved in ways that conform to their notions of how a compassionate human being should behave. In other words, if Meursault had cried at his mother's funeral, society (Meursault's peers) might have been more inclined to believe that killing the Arab was indeed an accident. But since Meursault was so cold at his mother's funeral and since his behavior is so odd in court, it is more difficult for them to believe that the murder was an accident.
The Prosecutor is well aware of this and well aware of the fact that Meursault doesn't conform to society's rules and strictures of behavior. Meursault didn't have a good relationship with his mother and that's why he felt little at her funeral. The Prosecutor uses this as an opportunity to frame Meursault, not as an honest albeit dispassionate individual, but as a cold individual clearly capable of murder. At the end of Part 2, Chapter 3, the Prosecutor says this quite bluntly:
"In short," he concluded, speaking with great vehemence, "I accuse the prisoner of behaving at his mother's funeral in a way that showed he was already a criminal at heart."
Seeing that Meursault felt no grief at his mother's funeral, others find it hard to understand him and certainly they find it hard to sympathize with him and consider that killing the Arab was a mistake. As the trial progresses, the indictment becomes less about the actual crime and more an indictment about Meursault's behavior and existential outlook on life.