John Green (the guy in those history videos I link to most Sundays) has the clearest and most succinct and accurate explanation of high health care costs in the U.S. The short answer is that there are a combination of things going on, not just one simple problem.
As Green points out, the government in the U.S. already spends more per capita on healthcare than do other developed countries. What that means is you take total government health care spending, divide by the population, and that's the per capita cost of health care to the government. That number is bigger for the U.S. than for Germany, Japan, Australia, the UK, etc etc etc.
But what he doesn't make clear is the total cost of healthcare, counting not just government spending but all of it, including health insurance, out-of-pocket expenses, charitable care, everything. The government's share of healthcare costs per person in the U.S. would cover all healthcare costs per person in Australia, France, the UK, Japan, etc.