Her mother’s heritage
Sam didn’t care about clothes or material things, and so she used to dress like a tomboy. Mrs. Banks, on her part, interpreted this as Sam being a tomboy and thought she didn’t care for her mother’s china set.
Growing up learning that “things were only things,” Sam didn’t care about having the china set, but what it represented. It was valuable for her mother, and Sam didn’t like Mrs. Banks acting as if it was hers and giving it away.