If libertarians want to argue that everybody should take personal responsibility for their own healthcare and the burden shouldn't be carried by the state - I disagree - but can understand the point.
If they want to make the case that universities shouldn't be funded out of the pulic purse - again I disagree - but can see the principle behind the argument.
However in order for any of these to make sense then surely you need to assume that everybody has had equal opportunities in life - not so if you remove free healthcare for children and privatise education fully.
It creates a class system whereby your education/healthcare from a young age is determined by that of your parents.
I say this as a healthy unmarried childless male