Surprisingly, the woman told the truth in such position, indicating the helpless and desperation situation she was suffering from that made her give up insisting keeping it as a secret.
When the woman said that she had a son, I have already guess that the boy is the man's son, for she loves her son crazily too.To some extent, her son represent her love to the man.
I am extremely shocked at this,for I have never thought that the man is the death child's father.As far as I am concerned,this is the climax of the story.