Mother Jones lays it out:
The biggest problem with Ryan's plan is that it doesn't actually control health care costs. It simply shifts the burden of paying for them from the public sector to individuals. Instead of the government going bankrupt trying to pay for medical care, it'll be individuals. That's all well and good for the rich, who might be able to pay for their own health care. But people who would have relied on Medicare are going to be out of luck. Medical costs wil rise much faster than the value of the voucher will. Ryan's plan seems to pretend that the problem isn't medical costs—it's just that the government is trying to pay for them. James Kwak is good on this:The implicit premise [of Ryan's plan] is that we have to screw ordinary people–or at least make them bear a high degree of risk–in order to save the government budget. But what is the government budget? It’s a pile of money that we contribute and that our representatives are supposed to spend on things we can’t buy for ourselves individually. I know that those representatives make mistakes, are borderline corrupt, etc. But Medicare is exactly the kind of program that we want government to provide–a program that shifts risk from individuals to the government, and thereby the country as a whole–and that’s why it’s so popular.
Other countries manage to keep their citizens healthy at a much lower cost than we do. They don't have to dismantle their social insurance programs to do it. Why should we?