Satella claims to love Subaru for "giving her light, showing her the outside world, holding her hand when she was lonely, and kissing her when she was all alone, essentially giving her everything". She states that she gave him Return by Death to kill her, however he refuses to do so, telling her that he'll save her instead.
Certain people, such as Echidna and Pandora, have referred to Emilia as "the witch's daughter", with Pandora also mentioning that she was of the witch's bloodline after seeing her power, hinting at some sort of connection between the two, though nothing has been explained.
It's worth noting that Minerva, Sekhmet, Typhon, Daphne, and Carmilla hate the Witch of Envy, not Satella. Echidna is the only one who hates her regardless but she can't do anything as the other witches would join forces against her.