The individual mandate was the worst thing about it. Suddenly, the federal government was making its citizens purchase a product that they didn't necessarily want or need as the cost of being an American citizen. IMO, that was wrong on principle.
I realize that the mandate is hard to defend as a libertarian, but here goes...
We allow for mandated auto insurance as a condition of driving a vehicle on public roads. I don't think many libertarians really have a problem with that. The idea is that the ability to buy and drive a car gives you an enormous power to wreak damage on others, both economic and physical injury. But you have a choice--if you don't want to drive a car, you don't need auto insurance. So there's no fight.
The young and healthy among us decide "hey, I don't need health insurance." They're young and healthy, and believe themselves invincible, and the vast majority of them probably won't really use their insurance much.
But... What happens when they're playing extreme ultimate frisbee and crack heads with someone, the ambulance is called, and they have to go do the ICU to stop a brain bleed? They're going to get care, because the hospital doesn't make insurance a gate to providing emergency care. These young people aren't given the choice "do you want to get care or die because you can't afford it?", they are just given care.
They get a $200,000 hospital bill after it's over, and what do they do?
Well, the young and healthy often don't have
assets, so they declare bankruptcy. And the hospital (and taxpayers, often), get stuck with the bill.
I would agree with young healthy people gambling with their own health care if we lived in a society that would kick them to the curb and not provide care if they couldn't afford it. (Not that I would consider that a compassionate society, of course).
But in the current society, they're not gambling with their health, they're gambling with the hospital's money. And when you're gambling with someone else's money, you get all the upside of winning (you get care if you need it) and none of the downside of losing (because you're not risking your own assets).
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Despite the above, one of the critical problems with Obamacare is that there was no option to JUST sign up for catastrophic care. They put a whole bunch of mandatory stuff into what an insurance plan must include to qualify, so there was really no way for young, healthy people to avoid signing up for plans they actually didn't need. So I agree with you there... But that doesn't change that the mandate can potentially be justifiable.