Universal doesn't imply nationalized

Last night, at Kaitlen and Matt's Halloween party, some of us were debating the merits of libertarianism as opposed to the welfare state. Take the argument "Everyone should have healthcare and education, so the state should provide it." Sounds like a reasonable argument. When you list out all the unspoken parts, the argument looks more like this:

1. Everyone deserves access to healthcare and education.
2. Only the state can guarantee that everyone has access to healthcare and education.
3. The best way the state can guarantee that everyone has access to healthcare and education is by nationalizing healthcare and education.
4. Therefore, the state should nationalize healthcare and education.
   

I wholeheartedly agree with Point 1. I will accept Point 2, since I don't know of any alternatives. The unspoken Point 3, however, is much more difficult to agree with. Nationalizing healthcare and education is certainly not the only way to guarantee access for everyone. Another way would be to give vouchers to people who couldn't normally afford private healthcare and education. There are still other ways it could be done.

Which one of these methods is best is a long discussion. My more immediate point here is that one can agree with Points 1 and 2 but not reach Point 4. Universal healthcare and education doesn't necessarily mean nationalized healthcare and education.

Correction: I originally attributed the above argument in quotes to Damon. His actual opinion is more complicated. Alcohol kills nuance.