Health care is a private good, not a public good. To see why this is, let us look at the definition of public goods.
Public goods have two main aspects. The first aspect is nonexcludability and second is nonrivalrous consumption. Health care does not have either of these aspects.
Nonexcludability means that the provider of a good cannot keep people from using that good. The classic example of this is national defense. If the government protects the country from invasion, it cannot exclude a few people from that protection because they do not pay for it. Health care is not like this. Doctors can easily exclude people from using their services. If a doctor performs surgery on one patient, no other patient benefits from that surgery. This is not a nonexcludable good.
Nonrivalrous consumption means that, when one person consumes the good, it does not mean that there is less of the good for others to consume. If I benefit from national defense, it does not reduce your ability to do the same. Health care is not like this either. A given doctor can only see one person at a time. There are times when people want appointments with their doctors and have to wait because the doctor has no openings for a couple of days. Therefore, health care does not have nonrivalrous consumption.
Because of these facts, we cannot say (in economic terms) that health care is a public good. Therefore, it is a private good.
This can be a personal opinion answer. I believe it is a public good. I believe we should have free healthcare before we have free schooling.
Why? For me, it's sort of an easy question when one considers that if you have two people, both needing similar lifesaving procedures done, both have the access to get it done by similar personnel at similar facilities. The only difference is the one with money has insurance, and the one without money has no insurance. The one with money is more likely to be able to get the procedure done.
We are going to grant life to the person who has more money to pay for the insurance and, thus, the medical care? Sorry, but for me, that's simply wrong. People are getting very wealthy at the expense of other's health. My father was an insurance agent. He used to tell me when he would cancel a person's insurance for the sole reason that their coverage wasn't "profitable" for the company. So, there goes their medical coverage and, thus, their health? I think that's wrong.
I can understand what my dad did. But the entire system needs to be changed. That person obviously still needed medical care. In the blink of an eye, they had none.
Palin liked to say that "death panels" would result from the Affordable Care Act. What's so different between that and what my dad did? Absolutely nothing. Thus, there were "death panels" well before the ACA. They were called insurance companies. How did they act? By cutting off insurance coverage because their company wasn't making a profit anymore. I even remember hearing of one family who just had a baby. They had healthcare through the father's company. As soon as the baby was born, they lost it. Why? Because the baby was born with a defect that the company doesn't cover. So, the family lost their entire coverage. Since when was a married couple having a baby supposed to be a negative occurrence in the life of a young married couple? That insurance company essentially gave the death notice to that baby. And it was all entirely legal, no government involvement.