SWICA recommends that you take out your own separate policy so that you start dealing with your own insurance arrangements and become more and more familiar with them. No matter whether you have separate or joint policies, upon reaching adulthood, you are responsible for your own insurance in any case.
One benefit of having your own policy is that you can set up your own account for any amounts to be credited (for example for gym memberships), and you alone can view and edit your data. The last point can be a drawback if your parents are still taking care of your health insurance. If this is the case, you can give one of your parents power of attorney.
If you stay on the family policy, your parents can continue to take care of your health insurance (with limitations*). This means that you will be unable to set up your own account for amounts to be credited, and your health information will not just be available to you. Your parents will be able to see where you have been treated and when, for example.
*Particularly sensitive data is not made available to the parents of adult children.