First of all, notice that there is NO Federal mandate for drivers to carry automobile insurance. The fact that some states require drivers to be insured says nothing about the Federal government's authority in this matter. The 10th Amendment of the Constitution clearly grants rights to the states which are not granted to the Federal government. To be analogous to automobile insurance, the Federal government should let states decide if they will mandate medical insurance or keep it optional, just as they do now.
Secondly, no state requires that everyone carry automobile insurance. Children don't need to carry it, and neither does an adult who does not drive. Carrying automobile insurance is a requirement to perform a particular activity, not a mandate applying to everyone, simply because you exist.
Third, the purpose of mandatory automobile insurance is not to protect the holder of the insurance, but to protect everyone else on the road. Those states which do require insurance do not require that you carry collision coverage. The only requirement is to carry liability coverage which protects anyone else on the road who might experience bodily injury or property damage as a result of an accident you cause. Without that insurance, and without the means to pay for that damage, you might cause an accident which costs someone else tens of thousands of dollars, and not be able to pay for that damage. The insurance you must buy protects the other driver, not you. In every state, you can choose to not carry insurance to protect yourself. It is completely acceptable to self insure against damage to your own car. If you do that, you are accepting the risk that you might wreck your car, and if you do, repairing it or replacing it will be at your own expense. Medical insurance is analogous to collision coverage, not liability coverage, because it does not protect someone else against damage you might cause. It protects only you. To complete the analogy, those people who have the means to buy medical insurance but choose to self-insure must recognize that if they need medical attention, they will have to pay for it out of pocket, and they can't expect for society to pay the bill for them.
Finally, many states do not require drivers to carry insurance. They allow other options, including self-insurance. The State of Texas Transportation Codes contain the following options:
SUBCHAPTER C. FINANCIAL RESPONSIBILITY; REQUIREMENTS
Sec. 601.051. REQUIREMENT OF FINANCIAL RESPONSIBILITY. A person may not operate a motor vehicle in this state unless financial responsibility is established for that vehicle through:
(1) a motor vehicle liability insurance policy that complies with Subchapter D;
(2) a surety bond filed under Section 601.121;
(3) a deposit under Section 601.122;
(4) a deposit under Section 601.123; or
(5) self-insurance under Section 601.124.Self-insurance is an option. So using automobile insurance to make the case that self-insurance should not be allowed is a flawed argument.
This is a common argument, which comes up almost any time statists attempt another expansion of the power of the Federal Government. The argument is essentially that the government is already exceeding its authority, so why not exceed it some more? Even if the analogy held in this case, that's not a sound argument. It is one which leads to tyranny.