From her birth, the most important thing in Bellatrix's life was family. Not because she particularly cared, but because it was so very evident that she had no choice except to care about them. They were the reason she was told to do anything.
"Bellatrix," her mother would say if she got her clothing dirty, if she spilled water at dinner, if she did not keep a small, polite smile on her face at all times, "is that any way for a Black to behave?"
No, Bellatrix thought, once she'd grown old enough to question such things. But it's the way a child should behave.