It’s not cheaper to be on your parent’s car insurance. The reason why parents end up adding their kids to their car insurance is that they’re worried that their kids will make a claim on their car insurance or they’re worried that their kids won’t have car insurance.
It could be cheaper to be on your parents’ car insurance policy, but it depends on several factors. If you have a car that’s a couple of years old, it’s unlikely that you’ll be able to get a cheaper deal by going on your parents’ policy than you would by going on your policy.