It cannot be explained because this is not one of the government's duties. If your teacher is pushing the position that somehow "free" healthcare is an obligation of the federal or state government, then throw the Constitution in their face and demand that they read it.
The best that your teacher will be able to come up with is the "general Welfare" clause. The problem with that argument is that the definition of welfare back then isn't what it is today. Not only that, but by "general" the Constitution means "everyone"; the rich, the poor, white, black, etc. and not just some disadvantaged group. The federal government should only be in the business of passing laws that benefit everyone, otherwise it's a more local issue that doesn't merit the federal gov'ts attention.
So along those lines, we can quickly see that "free" healthcare would only be something that applies to non-wealthy people and then would be disqualified under the original meaning of "general Welfare" and because it doesn't meet the requirements of that clause it becomes a State or even County issue. Good luck!
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