In evaluating our moral intuitions, we often reflect on whether this kind of phenomenology has resonance beyond other Western ("Western, educated, industrialized, rich and democratic (WEIRD)") points of view. Appiah's book focuses on honor killings and other "honor" practices, which seem only removable when the society in question gets mocked enough for engaging in them that they are dishonored, i.e. honor itself is used to halt the practice that was only kept in place to keep honor. Appiah argues, though, that since WEIRD societies focus on individual ethics and don't see a moral wrong by an individual as a stain against the group, that removes a prime mechanism for moral improvement at the social level.
Stated this way (and of course I'm sure there's more to it in Appiah's book), I don't quite get it. If we don't currently have horrific practices perpetuated in the name of honor in the West, then we don't need this mechanism to remove them. It would be nice if we had social mechanisms to encourage progress on (or dismissal of concerns regarding) alleged socially approved misdeeds like abortion, eating meat, and circumcision (none of which seem directly tied to honor), but the fact that we have a vigorous democracy with lots of parties speaking seems to give more hope of long-term resolution re. these issues (in the way that recent progress has been made re. gay rights and how concerns about interracial marriage have for the most part disappeared) than alternative social arrangements.
(Note: the image here is by Vlad Gerasimov.)