Miles, much like people confusing socialism and communism you are confusing corporatism and capitalism. Corportism is only possible when the government leverages the the market in favor of an industry.

The difference between the NHS and a private system is choice and freedom. We have a mix in the US of private and public and isn't really a good example for free market economics. Regardless if you don't see the difference in the government forcibly taking ones income to pay for a service and citizens involved in voluntary exchange I dont' know what to tell you. At the end of the day your policy preferences are based on mob rule empowering government agents to steal peoples income on their behalf. If your are ok with a worldview based on coercion then ok. I prefer a society based on voluntary exchange. I'm not anti-government at all I just don't think it should pick winners/losers or coerce its citizens. Unlike many functions of the government the military is actually an enumerated power of the federal government in the Constitution.