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Specifically, Tim is for the kids who had parents with undiagnosed trauma and mental illnesses. The ones who had to gentle parent their own parents. The ones that have to remain stable even when they can't because they are needed.
Dick is for the eldest children that feel constant guilt for how their actions affect the rest of the family. In success, you set a standard too high for them and in failure you're taking away resources(time, emotional energy, money) that should have been theirs.
Somewhere in between, relating to them both, is the youngest that has to be happy all the time for the family to function. The one that gets made fun of when you need a joke. But also the one that knows everyone's triggers and is always paying attention to everyone's mood. The one whose work is never recognized because no one else has to be home as much as them, everyone else gets a break but them.
Dick is for the eldest sibling while Tim is for the parentified children and I think that's the most important difference between them
Okay I'm thinking about Luke Castellan and all the reasons for his betrayal of the gods, and one that I personally have never seen talked about is his own parentification.
Cause he grew up with an unstable mother, meaning for the most part he had to raise himself and THEN he runs away and he meets these two girls, both younger than him and just as lost as he is, and he's found someone to protect in a way he never gets to be protected.
He gets to camp, and from there he's raising a grieving Annabeth BUT as time goes on and he gets older he gains more responsibility, and by the time Percy meets him, he's basically a parent figure to the ENTIRE Hermes cabin, as well as one of if not THE oldest camper in the whole camp.
He's constantly watching these kids beg for the gods'attention, both parental and otherwise, and seeking that attention in him, and of course he curses them. It is because of them the kids he cares about are hurting. And, more selfishly, it is because of them he has an emotional and mental burden of parenthood, when he never wanted nor prepared for it. Of course they're the villains.