In "A Good Man is Hard to Find," why does the Grandmother say the Misfit is one of her children when she only has one son?

The
grandmother, in a misguided attempt to appeal to the Misfit's non-existent sympathy, calls him
"one of her own children." She does not mean that she suddenly recognizes the Misfit
as her long-lost child in a literal sense; rather, she means that he is so familiar to her at
this particular moment that he could be her own child.

The grandmother makes
this kind of comment in response to a display of vulnerability by the Misfit. While talking
about Jesus, the Misfit has just displayed some emotional depth, as evidenced by the expression
on his face being "as if he were going to cry." Possibly, the grandmother may be
trying to deepen the emotional connection between herself and the Misfit so that he will feel
something positive towards her and let her live, but no matter her motives, her attempts to
create a bond fail. The Misfit shoots her when she tries to touch his shoulder and offer him
comfort, and he and Bobby Lee mock her talkative manner over her dead
body.