Why is US life expectancy so short relative to the amount we spend on health care?

Because of fat people.

There are several reasons the US spends so much more on healthcare. The US is the only developed country where most of the populace rely on for-profit insurance companies. Allowing companies to profit from an essential service drives up the price. Also having so many hundreds of different insurers vastly increases the paperwork and bureaucracy needed to run the system, further increasing the cost. The US is also among the few which puts no price controls on what drug companies can charge. Since most Americans pay for their insurance through work they don't realise the actual cost, as it simply limits the pay-raises they would otherwise have. Another reason the US pays more is the ease of filing personal injury lawsuits there. US law makes these very easy and puts very little burden on the plaintiff. As a result medical malpractice insurance has become extremely costly. New Zealand avoids this problem by not allowing any personal injury lawsuits at all. Instead we have a system called ACC where the government covers all medical expenses resulting from any kind of accident or work-related injury or illness as well as paying workers compensation if the person is unable to work while recovering. Thus there is no medical bill to pay, no lost income and no need to sue anyone. A major cause of the expense of the US system is the large number of uninsured people. US hopitals are required to give them urgent care, usually with the taxpayer having to cover all the costs because they can't afford it. All the prices have been set by the insurers and private hospitals, all set up to make a big profit, so when the person can't pay but the hospital must treat the govt. gets a big fat bill. Since only urgent care is free to the uninsured in this way, they put off treatment until it is an emergency, making that treatment much more costly than preventive care. The US insurance system is different to public systems in another key way, it looks after the best interest of the individual, not the public as a whole. Thus vast amounts of money are spent to sustain a person's last couple years of life. Public systems are utilitarian, they do what is best for society as a whole. So someone who is 40 and working gets a knee-replacement in a week and a 70-year old retiree waits several months. A Cancer drug that can treat the most common breast Cancer is free but one for a very rare type of Cancer is only partly covered. In NZ our govt. buys all drugs in bulk, all generic and only after the patents have expired. So we sometimes have to wait years after a miracle drug comes out before we can use it. If you don't want to take that chance people in NZ can always buy their own private insurance at much lower rates than are paid in the US. As for the shorter life expectancy, that is likely due to the higher poverty rate in the US compared to the other nations, its higher infant mortality rate (also likely linked to higher poverty) and higher obesity rates. The millions of uninsured who don't get preventive care also probably drive the age down. The US would probably save money if it had a public health insurance scheme like most developed nations. But I doubt the life expectancy would go up much without addressing the wider problem of poverty where about 20% of the US population is living below the poverty line.

Because so much of the cost does not go toward health care because we have a free market health care industry.