Until a person has decided to become independent, as in providing for themselves and whomever else they choose to do so for, they are subject to the rules and ideals of the people sheltering, feeding, and providing for them (in this case, their parents). This is not necessarily about parents knowing, this is about the person who holds guardianship or who is providing knowing; until the person (in this case minor) is of legal age or is independent, their parents/guardians have the right to anything they choose, so long as it conforms to state and federal law.
Abortion is every woman's right and is a very personal choice. Regardless of the woman's age, she should have the right to an abortion without interference during early pregnancy. Requiring parental notification or consent can prevent a young woman from having an abortion, which will affect the rest of her life and the life of the child she may be forced to have.