When discussing whether a particular government program is a good idea, it's important to first separate the merits of the program from the issue of redistribution of wealth. For instance, many advocates of universal health care see it as a way to provide services to those who cannot currently afford to pay for them. To the extent that might be true, the 'benefit' is merely redistribution of wealth by a different name.
In such a program, there are winners and losers. Those who pay less than their proportional share of taxes may benefit - the government is giving them something that costs more than the increase in their taxes. Those who pay more than their share of taxes are the losers - their taxes will increase by more than the value of the services that the government is buying on their behalf. As long as there are more winners than losers, the program might win enough support to be enacted.
There are three problems. The first is a moral issue: what right does the majority have to appropriate the property, income, or livelihood of a minority? It is generally accepted in our society that those with more income should pay more in taxes, but there is no clear limit to how far that principle extends. When does it exceed the bounds of fairness?
We have a situation where the vast majority of taxes are paid by a very small minority of our citizens. This means that for most people, there is very little connection between the privilege of receiving a government benefit and the responsibility of paying for it. Government benefits feel like 'something for nothing'.
The second problem is organizational: the government may not be the most effective and efficient mechanism for managing the process of creating and/or delivering the service in question.
The third problem is that the establishment of a government program to provide a broad-based service has the effect of dramatically reducing the availability of other choices. Since everyone has to pay for the government service whether they use it or not, only those who are wealthy or highly motivated will pay a second time to make use of a non-government alternative.
This has the effect of dramatically limiting the choices available to individuals. If the government service is not well suited to the needs of the individual, there is little that the individual can do. This has the effect of making people helpless dependents of the government.
The real question is whether the average person would be better served by such a program. For the sake of this example, an average person is someone who pays exactly their proportional share of the total tax revenue collected by the government. Therefore, their taxes would go up by the same amount that the government spends on their health care.
Would this hypothetical average person be better off giving their money to the government so that the government can then pay for their health care? Would they prefer to have fewer choices? Is the government likely to be the best and most efficient mechanism to organize and pay for health care services? It's hard to argue that this is likely to be the case for most people.