أَفْشُوا means “spread widely.” The instruction is not simply to perform a greeting ritual among a favored group; it encourages beginning encounters with a message of peace and goodwill. A greeting of salam carries a prayer for the other person’s safety and therefore belongs with respectful, truthful behavior.
For example, someone may warmly greet close friends but ignore a newcomer. Spreading greetings challenges that exclusion. Saying words of peace while subsequently belittling or harming someone would contradict their ethical purpose.