ok so
Obviously she jokes about being the best/favourite Hephaestus kid, but actually doesn't believe it.
In her eyes, there's better out there- Leo who completed the quest, Charles who sacrificed himself, and literally everyone else she views as preferred to her.
Not only does she feel like that though, but she denies it to herself. She never had strong parental figures because her mum sucked, and even feels like her siblings hates her sometimes because either she had to act like their guardian and they weren't used to discipline, or because she couldn't handle it and took a break meaning they felt alone.
Because of her shitty mum, she just secretly wanted approval, and even though she'll constantly deny it, deep down all she wants is approval from some form of parental figure
