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A week after Matthew and Bobby were born, Annabeth realized that the way their dad looked at them was the way she always wished he'd look at her.
They were simple, easy. They were mortals- Twins, yes, which was abnormal in its own right, since most kids were not twins- But still mortals.
They didn't pose danger simply by existing. They didn't attract monsters or other unfortunate circumstances. They were just kids, that's it.
And her dad wanted them, whereas he'd never seemed to want her.
At first, jealousy took hold and she acted out to earn the attention that she'd so rightfully deserved (and that had been unfairly redirected to the twins).
This didn't work, though, and just served to annoy her father and piss off her stepmother, earning her many annoyed glances from the former and a few beatings from the latter.
Once it became clear to her that acting out would get her nowhere, she switched tactics, doing her best to show love to her father in hopes he'd return it.
He didn't.
He was always just too busy with the twins (she found it bitterly amusing that he'd never been too busy with her when she was their age).
It was a hard pill to swallow, that he didn't love her the way he should. The treatment from her stepmother definitely didn't help.
Maybe she should just run away...