On Public Goods
From what I've seen is that many libertarians see the term "public goods" and think "things provided by the government". So things such as garbage collection, water, sewer, fire department and so on. This redefinition seems to be quite common as the actual definition causes problems with the libertarian ideal.
At this point it is probably a good idea to describe what economists and political scientists actually define the term "public goods" to mean. Strictly speaking a public good is something that once provided, you can't prevent anyone from enjoying the provision of that good. As an example I present the lowly streetlight. Once a streetlight is in place and operational, there is no way of truly preventing anyone from enjoying it's use. The light turns on, throws light everywhere and even if you don't want the guy across the street from using the light, there's little you can do about it.
Now libertarian philosophers have written that there's truly no such thing as public goods. They do this is as libertarians like to argue that the market will solve all problems, but the market fails when it comes to the provision of public goods. Since there is no way to prevent someone from using a public good, there is no incentive for anyone to actually pay for a public good. Since no one is going to pay for the public good, it will not be provided. So using our streetlight example, streets would be dark (and it could be argued that the streets themselves would not be there in the first place). Libertarian ideology has no solution to what is called the free rider problem when it comes to the provision of public goods, so like an evangelical Christian confronted with evidence for evolution, the libertarian either simply denies that public goods exists in order for their beliefs to remain internally consistent or changes the definition of public goods to mean things provided to us by the government.
This leads us to the popular joke "How many libertarians does it take to stop a panzer division?" as national defence is a public good. If an army is to be raised through voluntary donations, how can you stop that army from defending all the houses around the free rider but not the free rider's house? This causes quite the dilemma as many evangelical libertarians believe that all taxes are theft. This prevents a tax from being imposed on someone who doesn't want to pay for defence (or some other public good). This would force the libertarian (in his language) to initiate force on someone, in complete contradiction to the libertarian ideal.
Of course this isn't the only criticism of libertarianism out there, but it is one where I find it interesting that someone will tie their perceptions in knots to the point of denying reality in order to hold onto a deeply cherished belief.
For other critiques of libertarianism check out: