Admit it - you felt sad for Dren when Elsa took the cat from her. Though, since Dren kills the cat immediately after getting her back, that feeling may not last.
Arguably that makes it even more sad. Dren imitated the behaviour of her bipolar, abusive mother there, as a revenge for essentially comparing her to a pet animal. No-one ever taught her to control her impulses or to understand why petty cruelty isn't OK.
As an added justification, Dren may have also been jealous over Clive.