Simply because everyone having Auto Insurance is a 2+2=5 benefit. When all drivers have insurance, no individual must fret about paying for the others care after an accident. Therefore, premiums are lower for all involved, and insurance companies are able to pay out more in repairs because of the larger customer base, a win-win for all involved.
However, both Homeowner's Insurance and Medical Insurance benefit the individual. If you can't rebuild your house after it burns down, or can't afford that heart surgery, it doesn't help or hurt me. So while Auto Insurance is mandatory just about everywhere, home Insurance isn't required in every state, and Health Insurance is left to the individual in most states.
Mandating health insurance is a "Government knows best" action, while Auto Insurance is a "Everyone pitch in a build a new road through town" action, where everyone will benefit more if everyone pitches in.
Does the government know best? Well, you'll say, "Only if a Democrat is running it," I'll bet