IIRC, the only people she did talk about her family to were Babs (and Jim after she'd saved him in her introductory scene, to explain who she was to Cain), occasionally Batman, and Steph. Only with Steph was it casual, the other cases were always deeply meaningful, and I'm not sure she ever was the one who started the subject with Babs.
Maybe she can adapt her talking about family to how she perceives the people she's talking to feel about family, that'd explain why it was such an important subject when she was with Batman even if they rarely spoke directly about it, or maybe she changed her views since then. I'm not inclined to giving this the benefit of the doubt.
Why would she tell Katana about something like this?