What childhood memory does Beneatha share with Asagai? Why does she tell this story?

In Act III of A Raisin in the Sun, Beneatha reveals to Asagai the original reason she wanted to become a doctor.  She tells him about seeing a young boy named Rufus who had a sledding accident--he crashed and broke some bones and had a large cut on his face.  What amazed her as a child was "that was what one person could do for another, fix him up--sew up the problem, make him all right again."  She also says, "I always thought it was the one concrete thing in the world that a human being could do. Fix up the sick, you know—and make them whole again."  Beneatha's desire to become a doctor stems from this incident, as does her idealism that has so attracted Asagai to her.  But at this moment in the play, Beneatha has lost that idealism because Walter Lee has given away the insurance money, and she does not see a way forward to achieving her dream.