As I have said about the abortion debate, things become clear when you lay out the logic of the situation (unless, of course, the one or more sides of a debate bring out the "unprincipled exception" or resort to illogic or dishonesty).
This article on a Dutch politician who wants to penalize stay-at-home mothers who have received government-subsidized educations shows why government subsidies are often a bad idea. If the government pays for something for you, it at some level owns you. It allows itself the foot in the door to begin making personal choices for you in order to recoup its investment. Can you imagine what this might entail in terms of health care in a socialist single-payer health system?
Of course, some liberals would get around this by stipulating a right to a certain standard of living without any concurrent responsibilities (i.e. I have a right to do whatever I want and to make the responsible people pay for it). This reminds me of the old cartoon (I think it was from the Far Side), which showed the epilogue to the story of the ant and the grasshopper: it showed the ant dead, its head smashed in by the grasshopper's fiddle, while the grasshopper made off with the ant's grain. In any case, the reason this won't work is that eventually the responsible people will stop working because they get nothing out of it, and totalitarian control will need to be imposed to keep the whole shebang together.
But either way, government funding implies government control. And that is the lesson of this story, and why government funding is so dangerous.
That is all.