Whether or not a minor can get their own car insurance is a difficult question to answer, as the laws regarding this vary greatly from state to state. Generally, a minor, defined as someone less than 18 years of age, can obtain car insurance coverage for a motor vehicle as long as a parent also signs the policy. So, a teen driver can have their own auto insurance - but not without the help of an adult. Teens that live with their parents are usually just added onto their parent's insurance policy.
The underlying reason minors are denied their own insurance is that most state laws prevent a minor from entering into legal agreements, which includes signing insurance contracts. Most states won't even allow a minor to be the sole owner of a car. A teen can purchase the vehicle, but must have a parent sign the title and registration, along with the car insurance policy.
These laws vary in each state. For example, Texas has no minimum age limit for the ownership of a vehicle. However, even though a minor can own a motor vehicle, the insurance companies are allowed to place age restrictions on who they choose to insure, and usually charge outrageously high premiums for teen drivers. In Ohio, the Bureau of Motor Vehicles requires a child's parent or guardian to complete a minor consent form in order for the teen to receive the title of a vehicle. Then, the parent or guardian must appear with the minor in front of the Clerk of Court to actually go through the title process. The best place to find out the specifics for each state is the Department of Motor Vehicles and insurance regulator for that state. Though the laws regarding minors, car ownership and car insurance change depending on which state you reside in, most laws and insurance company guidelines only allow a minor to have a car insurance policy if the said policy has been signed by his or her parent or guardian.
One point to consider, though, is whether or not it is even beneficial for a minor to have a separate car insurance policy. On the one hand, keeping a teen on an adult's policy will significantly reduce the teen's premium. On the other hand, teen drivers are very risky and all it takes is one major accident to negate a lifetime of good driving credits for their parents. So, it can be better to get separate policies and exclude the liability of the minor.
In general however, the laws and guidelines are there for a reason. It's worth major consideration when a teen driver wants his or her own insurance policy.