Why does Miss Emily stop teaching china painting?
When Miss Emily was in her forties, she gave china-painting lessons to the girls in the town for a period of six or seven years. That was eight or ten years before the aldermen called on Miss Emily to try to make it clear to her that she must begin paying her taxes. What caused her to start giving lessons is an unanswered question. About ten years had passed since the death of her father, and her relationship with Homer Barron had been over for about eight years. Perhaps Miss Emily had sufficiently recovered from her loss of her beau and desired human interaction, or perhaps she felt the need to make an income. Whatever the reasons, the town humored her, sending their daughters to Miss Emily more as an act of charity than for what they hoped to gain from her. Thus the "daughters and granddaughters of Colonel Sartoris’ contemporaries" brought her their quarters as if they were bringing money for the Sunday School offering plate. These representatives of the traditional community did their duty toward one of their own despite how odd she was. They were following the same spirit that had caused the town to forgive Emily's taxes each year.
However, when "the newer generation became the backbone and the spirit of the town," Emily no longer had a steady supply of china-painting pupils. The new community members did not think they owed Miss Emily anything. Thus the same spirit that led the aldermen to call on Miss Emily to explain the new requirement for her taxes also led to Miss Emily having to give up her china-painting lessons. It does not seem as if she wanted to give them up, but rather that people stopped feeling any obligation to send their daughters to her.
Miss Emily's cessation of the lessons is indicative of the distancing of the whole town from her, as well as the changing values of the town. In older days, the town was connected, cared for its members, and respected its elders. This dying art of china painting is one more example of the changing values.
It is stated that she was in her forties when she taught the china painting. She was in her thirties when she "married"/killed Homer. So I think that accepting children into the house 10 years after killing Homer was sort of like having the kids she would never bear because her husband was unable to pregnate her. They were in fact the only ones in the house besides Tobe.