While I will almost always advocate for a market based economic approach to allocating resources, health care is not an area where the profit motive should dominate decision making. Simply put, the end product is a patient's health. Private health insurance has a conflict of interest between the insurance company and the insured which will be resolved in favor of the insurance company a majority of the time.
Let me paint a hypothetical picture to illustrate this point. Insured makes a claim with the insurance company, which is a publicly traded company. Because the insurance company is publicly traded they must turn a profit and increase their profits to maintain their share price. In order to make a profit they have every incentive to either
1. Deny the insured's claim, or
2. Delay payment to increase the possibility the insured will drop his claim
There are numerous stories about an insured making a routine claim only to be inundated with paperwork, or being told the policy doesn't cover that procedure, or being told the insurance company has to look into the claim to see if the insurance company can make a payment. In any of these situations the central idea of insurance -- to provide some safety for the insured at a specific cost -- is compromised.
Read the entire article along with the charts that he uses. It is an excellent market-based argument for national healthcare.