So you are comparing food to insurance. Maybe part of the problem here is that people keep conflating government insurance with government-run health care. They are not the same. What's happening here is that the government is seeing a product that the private market is not providing, but society has deemed desirable for everyone to have. That's a pretty clear prescription for a government option (like USPS).
"Starvation insurance" is indeed a bad idea. So is "insurance" for routine care. It costs a relatively predictable amount of money to have a routine annual blood test and physical. Why can't I just pay that money myself, instead of paying an insurance company to pay that money for me? And if I can't afford it, instead of having the government set up an "insurance" company to buy me doctor visits and a dental plan, why can't they just give me vouchers for that too? Save the "insurance" for stuff that actually makes sense to insure against--things like hospital visits and so forth.
As for how health care is different from everything else, it's very expensive sometimes, and society has kind of decided that everyone deserves a basic level of care regardless of the ability to pay. By that I mean people will generally respond negatively to a statement such as "If you can't afford it, you can't expect to receive treatment when you break your arm." In contrast I think it's pretty reasonable to say "If you can't afford it, you can't have a car."
I don't think the government should run a health care monopoly, but there are significant flaws in the market system that require government intervention in many cases, and health care is certainly one of them.