“If the daughter of a man who is a Kohen will be defiled through having illicit relations, she has disgraced her father and should be burned.” Rashi explains, “She has disgraced the honor of her father. People will say – Cursed be the one who fathered and raised this child.”
From here we see that a person must live up to the prominence of his parents. He cannot say, “I can be who I want to be although my father is a Rav, Rosh Yeshivah or someone important in the community.” He must act in accordance with their status. We see this from the fact that the daughter of a Kohen is burned and does not receive the typical punishment of strangulation that a regular woman who is Mezaneh receives. She must live up to the fact that her father is a Kohen and has a greater level of Kedushah.