1) Private insurers are businesses that must grow. Their inclusion in any national program almost guarantees endless cuts in service, and endless hikes in costs to the public.
2) Private insurance businesses have motive and duty to provide as little service as possible at the highest price possible. This is an adversarial situation with the public.
3) A significant chunk of what is ostensibly customers' health care money goes to contributions to political candidates that many people may not care to support. Mandatory purchase of private insurance would have our government---our sworn and paid representatives---compelling citizens to provide revenues to candidates preferred by private insurers. There is no Public Interest health-related justification for mandating this part of an insurance policy.
5) Large percent of the cost of a policy goes to other non-health-related expenses such as advertising, CEO bonuses, corporate jets, business conventions, and corporate headquarters upkeep. No health-related justification exists for mandating that citizens pay for that along with the actual health benefits.
6) For-profit insurers, using revenue collected from customers, invest in all sorts of private businesses, many being among the most health-damaging ones, including cigarette manufacturing, pesticides (including many tobacco pesticides), dioxin-producing chlorine industries, genetically engineered crops, and so forth. This creates a conflict of interest in that insurers would be inclined to ignore or play down harms caused by their investment properties. This conflict motivates insurers to blame, as a distraction and PR tactic, every non-industrial thing they can think of for causing diseases.
These insurers also invest in sweat-shop operations, military contractors, and union-busting firms. Mandating that anyone contribute to any of that is an affront to all citizens who have been harmed by, or who oppose, those industries.
8) For-profit insurers, still using what was ostensibly customer's health care money, may invest in businesses that compete with a customer's own business or private investment property.
9) For-profits invest in businesses that a customer may disapprove of for moral or religious reasons. A mandate to purchase services from such an insurer would compel some people to violate their own beliefs.
10) For-profits invest in pharmaceuticals, thus creating a conflict of interest in that such an insurer would use its power to favor drugs from its own investment holdings over others that may be cheaper, more effective, or safer.
This conflict would also prompt an insurer to be lax in checking, or warning about, insufficiently-tested or harmful drugs....its own investment properties or others. After all, they can't open this can of worms at all lest it negatively affect them. This syndrome virtually guarantees that an insurer would oppose use of natural, un-patented remedies.
11) Mandates to purchase private health insurance are notably different from mandates on car owners to buy auto insurance. One may opt out of that requirement by simply not driving. But with health care, those in certain income brackets where "having" insurance is to be mandated will have no options except unacceptable ones---to a) leave the country, b) deplete assets to avoid the obligation, or c) die.
12) Mandates force people to speak to private insurers, an apparent violation of the Fifth Amendment---especially regarding the above-noted parts of the program that have no justification on health care grounds.
14) When the government subsidizes private insurance for low income people, much of that money will STILL go to the non-health-related costs ---including the investments in god-knows-what, and including big campaign contributions to political candidates.