People with higher incomes might complain that there money is going to other peoples' health when it should be going to theirs. A universal health care would mean an increase in taxes, it would also mean that there would be more rules and regulations for people to follow so their freedom of choice would be effected.
It is not fair for some to be sick and others well. Especially if they do not have enough money to get treatment. Mathematically the only way to help those that are the worst off health wise is to do a universal system. The single payer systems are not a good deal for the buyer and the insurance company can not offer much coverage due to high statistical risk.