Chimamanda Ngozi Adichie, the best-selling Nigerian author, wants American readers to know that African writers don’t just write about Africa’s problems. “When we talk about the developing world, there’s this idea that everybody should be fighting for the poor,” she says. Though it might seem obvious to point out, she adds, “people are diverse, and there are different things that are going on with them.”

She calls it the “danger of a single story”—the idea that people living in certain areas of the world all have one kind...