I revised this chapter, and probably will revise most of them. I think I will leave the later chapters as is, but this needed work so…enjoy the new version.
Hermione Granger was never one to let the biases of other people affect who she was, or how successful of a person she was. The rude taunts of "Mudblood" didn't really affect her self-esteem at all, and maybe it was because she simply knew she was better than them. I don't think we will ever know the answer for sure, but blood status never meant she wasn't capable.
While she wasn't one to let it hurt her self-esteem, it certainly played a role in who she wanted to become, and her desires. I guess you could say she wanted to be a role model; someone muggleborns just discovering this new world could look up to as a figure. She hoped to be the reason they believed in themselves, and their powers, without giving into the bias.
When she looked in the mirror, she saw a thank you note from a Muggleborn student whose life she had affected. Hermione wasn't all about the grades if you looked close enough.