Dee seems to have hated the old house because it represented everything from which she wanted to get away. Mama says that, in her memory of the night the house burned,
I see her standing off under the sweet gum tree she used to dig gum out of; a look of concentration on her face as she watched the last dingy gray board of the house fall in toward the red hot brick chimney. Why don't you do a dance around the ashes? I'd wanted to ask her. She had hated the house that much.
Given Dee's reaction to the next house that Mama and Maggie live in, and the new house's relative similarity to the old house, it seems as though she was embarrassed by the old house. She wanted to get out, to get an education, to be "more" that what she perceived her mother and sister to be, holding them and the place she came from in contempt. Mama continues,
I used to think she hated Maggie, too. But that was before we raised money, the church and me, to send her to Augusta to school. She used to read to us without pity; forcing words, lies, other folks' habits, whole lives upon us two, sitting trapped and ignorant underneath her voice.
Mama feels that Dee used her education to wound them, to trap them and make them feel stupid. Mama only went to school through second grade, and she admits that Maggie has never been bright. She even says that "Dee burned [them] with a lot of knowledge," linking Dee's behavior toward them with the burning down of the house. Dee was both embarrassed by their ignorance as well as reveled in her intellectual superiority over them.
Further, Mama refers to the fact that Dee had few friends as a child because she treated them similarly, with her "scalding humor that erupted like bubbles in lye." Again, Dee is compared to something that burns, that damages. Therefore, it appears that Dee hated that house for the same reason that she wanted to get away from her family: they all represented the same thing, a past of which she was ashamed (for the better part of her life), a past which, even now she doesn't understand or value for the right reasons.
Moreover, all of the references to Dee as something that burns -- even the dress she arrives in consists of "yellows and oranges enough to throw back the light of the sun" -- seem to imply that she might have actually been responsible for the burning of that old house. It is notable that she was standing calmly by her tree, but Mama seems to have been barely able to save Maggie. On top of this, Maggie still bears the burn scars from that night, much as she bears the emotional scars of having been burned, figuratively, by her sister for her entire life.