Even if you’re listed as an additional driver on their policy, you can still get your own car insurance. If you are no longer living with them, simply ask them to remove you from their policy. However, if you’re away at school and under a certain age, some insurance companies require that you be listed on the policy, regardless.
Something to keep in mind is that most car insurance companies and states require that the registered owner is the named insured on the policy. If your parents own the car you drive, you’re still required to remain on their policy.