Single-Payer involves loss of an entire industry of the free market - the health insurance industry, through all health care being paid for by government - and therefore I see it as socialism. While it is hardly the only thing that openly socialist states do to live up to their label, it definitely and unavoidably opens the door to becoming a socialist state, which should not be tolerated in this country.
What need do we have for a health insurance industry? All it does is profit off of sickness, and somehow challenging the notion that these companies provide any value or purpose, besides designed to be a mechanism where vast sums of wealth to the people at the top of insurance companies, is socialist. The American healthcare system is one of the prime drivers of inequality, and I'd be happier if it was done away with altogether.
