Every time the grandmother told the misfit that he "did not have common blood," she was trying to

become less selfish
save the misfit's life
save her own life
become friends with the misfit

Every time the grandmother told The Misfit that he "did not have common blood," she was trying to save her own life. This statement is taken from "A Good Man is Hard to Find" story written by Flannery O'Connor in 1953 about a grandmother and a serial killer named Misfit. This statement is said by the grandmother to manipulate "The Misfit" when "The Misfit" attempted to kill her family and her.