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"How does Aaravos care about Claudia when he’s manipulating her?" The thing is that Aaravos, for as much as he clearly does care about her and views her like a daughter, is way too blinded in his revenge for Leola to not continue having Claudia as his pawn in his grand scheme of things like he does care for her but his vengeance for Leola will always be his topmost priority.
Aaravos has even said that Claudia is his only light in this world and I do think that since he was trapped in a mirror for THREE CENTURIES without anyone nor knowing when anyone would come and find him plus his clear longing for wanting his daughter back plus the fact that everyone else hates him and fears him would make him desperate enough to the point that he literally drove Terry away from Claudia to make her dependent on him so she– really the only person he has left– wouldn’t leave both because he’s genuinely attached to her and because she’s an important pawn besides it’s clear that the father daughter dynamic had caught him by surprise/wasn’t planned and you can tell from the early seasons that she was always meant to be a pawn that he can’t afford to lose.