This is a great question. The role of family is central to the novella in two ways.
First, as the story progresses, we realize that Kino needed money to get the medical attention that Couotito needed after his scorpion bite. So, the whole plot of the story really is about the importance of family and a father's love for his son. This is also a part of the tragedy, because in the end the Kino's love is transformed into greed, which is the second point.
Kino's discovery of the pearl not only made him want to get a cure for Coyotito, but he also wanted wealth for his family. Here is one of the most important quotes of the book:
"In the pearl he saw Coyotito sitting at a little desk in a school, just as Kino had once seen it through an open door. And Coyotito was dressed in a jacket, and he had on a white collar and a broad silken tie. Moreover, Coyotito was writing on a big piece of paper."
We can see in this statement that Kino saw the pearl through the eyes of greed. Truth be told, everyone else did as well. People were willing to kill Kino to get the pearl and Kino was willing to kill others as well. However, the starting point was to find Coyotito a cure.
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