It's a small thing, but she just proved to her father that she doesn't have to be a Herald to accomplish something important, he realized.
No doubt Eric started gambling in an attempt to prove to his father that he was a winner.
Prove it to myself, to my father, to Bea, to the whole world.
"Hayes would need to prove himself to his father."
Think of what he did to prove himself to his father.
He must prove himself to his father by saving Gino's life.
He did not have to prove anything to his father or to himself.
"He wanted to prove himself to his father," she said.
Thus his strong desire to prove himself to his father and older brother.
His dream is to prove to his father that he did not need to get ahead.