In Harper Lee's To Kill a Mockingbird, Chapter Thirteen's quote regarding "women's work" applies to Atticus and his attempt to console the children.
In Chapter Thirteen, Aunt Alexandra comes to stay "for a while," though Scout points out that this is not necessarily a "visit"...
"For a while" in Maycomb meant anything from three days to thirty years.
Soon it is apparent that Aunt Alexandra's stay will be an extended one. She becomes deeply involved in the women's circle of Maycomb, having ladies to tea and passing comments on the residents of the town as if they were long-standing neighbors. She also becomes uncomfortably more involved in the lives of Jem and Scout. One day Jem mentions Cousin Joshua who had gone crazy and created (based on Aunt Alexandra's response) something of a scandal.
Aunt Alexandra is not pleased to hear this, and takes her concern to Atticus. One evening while the children are together in Jem's room, Atticus arrives and tries to speak to them, but he seems very unlike himself. He tries to impress upon the children, at his sister's insistence, that they are not "common."
Your aunt has asked me to try and impress upon you and Jean Louise that you are not from run-of-the-mill people, that you are the product of several generations' gentle breeding—
Alexandra's intent may be a lesson in their cultural roots, but it includes her desire too that Scout act like a young lady and Jem, like a young gentleman. Perhaps what frightens Scout so much, beside the fact that Atticus is speaking to them in his business-like "lawyer's voice," is that some how they feel they are now not good enough, whereas Atticus has never been concerned with these things. It appears that Atticus is not speaking from his heart, and they are "stunned" and confused.
When Atticus speaks curtly to her, Scout begins to cry. Her father seems like someone else—not the man she knows; but then he stops and assures them that nothing is going to change—that they should forget about it all. He is seemingly angry with himself that he ever agreed to speak of it in the first place.
Atticus leaves the room, but then opens the door again.
As Jem and I stared, the door opened again and Atticus peered around. His eyebrows were raised, his glasses had slipped. "Get more like Cousin Joshua every day, don't I? Do you think I'll end up costing the family five hundred dollars?"
I know now what he was trying to do, but Atticus was only a man. It takes a woman to do that kind of work.
Two things strike me here: that there are two kinds of women in Scout and Jem's lives. There is Aunt Alexandra who pushes to get what she wants without concerning herself with the feelings of children. She is powerful, but doesn't seem to have any heart—only a social consciousness. On the other hand, there is Calpurnia: she is the only mother Scout has ever had, and Jem barely remembers their mother who died when they were young. Calpurnia is more powerful: she can mend wounded knees and wounded hearts.
As Scout makes this note, we see the differences between the two women, but this also may be foreshadowing—for Chapter Fourteen finds Aunt Alexandra ready to fire Calpurnia.
Scout believes that while Atticus tries to cheer them, soothing bruised hearts is women's work...a mother's job—and ironically, the woman best suited is not the one who believes herself to be socially superior, but the one who cares for them not as the "hired help," but as a mother.
Scout means that she knows her father was trying his best in telling them that they should learn to behave better, however he was trying to fill a place that he could never fill. This indicates that Scout believes that it will only be reasonably right if a woman (a mother) were to do this work.