Why does the U.S. Affordable Care Act penalize those without health care?

The basic premise (and goal) of the ACA is to make sure that EVERYONE has healthcare coverage from some source.

Since the law did not provide for Universal (i.e. government-sponsored) healthcare for all residents, it required some mechanism to force people to enter the healthcare system.

That is, a healthcare system works best like any other insurance pool - you need a large number of people not currently using the system (i.e. receiving benefits) to help pay for the smaller number of people who do (i.e. need health care). This allows everyone to share risk and receive proper benefits if they need them.

The other question is whether or not it should even be permissible for a person NOT to have health coverage. It is extraordinarily unlikely that a person will never need non-routine healthcare in their life, even before they get old. Since an uninsured person passes on a large amount of the cost to treat them to everyone else, you have the sense of "freeloading" (i.e. using services others pay for with no payment by you). Put it another way, since we don't allow hospitals to refuse treatment based on ability to pay, why should we allow people to receive treatment without payment?

In the end, the PPACA is designed to try to make sure that everyone has some method of obtaining healthcare at a reasonable cost to them (the "Affordable" portion of the name). The penalty is the "stick" portion of the "carrot and stick" design, to get people to buy into the insurance pool, even if they don't need it right now. Because, they absolutely will need it sometime in the future.