liberalism doesn't really expect the government to help people that much, only to a very limited extent.  Think of when Jefferson said 'the best government is that which governs least', that is the general classical liberal view of the state.  They believe in a nightwatchman state which just provides protection for individuals rights to life, liberty and property and maybe some public goods, which cannot effectively be provided by the private sector.  Or think of John Stuart Mill's harm principle, where the state can only intervene in one's life or actions to prevent harm to another.  Liberalism doesn't expect government to do much for people; hence why libertarianism is really just a radical strand of neo-liberalism.

Extreme individualism is the pathway to Anarchy and chaos. In order to prevent anarchy and chaos a limited government must protect society with military and ensure law and order is maintained.

I don't think people are quite understanding how anarchy would work. In essence, anarchy would be perfect Communism, requiring an equal-ish balance of all things for all people, and that there would be no need for political power because no-one would be in want, having their needs met by the perfect communal society where all people are as siblings

It's much more utopian than libertarianism, which advocates a state-of-nature system with the most minor of implications in place to keep it from becoming chaotic (libertarianism having different beliefs about where human nature goes wrong) Libertarianism is more realistic, but still utopian to the point of unfeasibility.

That's classical liberalism which is today's modern Libertarianism.

I believe there was much unity in the 19th century between Anarchists and Communists.  What I believe happened was through the likes of Lenin, there was a drive on the Communist side to bring about the end of capitalism via the use of the state.  Appauled by this, the Anarchists split.  

In regards to the discussion here, there are people who can go anarchists for a number of reasons, and have a different view of property, and other things also.  

It is my take that it is important for people to separate the role of government, from the shape of society.  They are separate.  If someone doesn't separate this, then they end up not seeing the ends and intentions of people.  

Someone can be anarchist for a lot of reasons.  Someone who is anarchist can believe government gets in the way of them filling their own potential, and the potential of top performers.  Others seen government as the tool of the elite to oppress the masses, so getting rid of government means that equality will happen.

The thing about anarchy is that it doesn't work. Anarchy isn't a system of governance, just a state without there being coersion on top to force conformity to standards of a society as a whole, and the aquisition of resources by coersion in order to reallocate them, so society can be better off.  You can't look to anarchy and find anything about the end state desired, because it is a negation (like atheism) based on the lack of something.

I have said that libertarianism is pragmatic anarchy, in that it will tip the hat to sometimes there being a need for the use of coersion for the better state of society.  Libertarianism seeks to minimize it though, as opposed to anarchy which seeks to eliminate it completely.  And this gets back to my original question about what arguments Libertarians have against abolishing government, rather than seeking to limit it.

There are people who organize themselves without the use of coersion and force to hold things together.  They do this, based on a number of things.  So, I can take what you said and change it to read: Extreme individualism is the pathway to Anarchy or chaos.  Someone who believes in anarchy from a philosophical or political view will often argue that anarchy is the only way to have real order in society, an order than rises up from the bottom, as opposed to architected from the top.

It's because Lenin (rightfully) knew that human nature acts agaisnt working in an anarchist co-op type way. 

Therefore he thought a Strong government was needed to beat individualism, ethinicity and nationality out of the common person changing everyons sociology from the base of it to be based more towards collectivism. (whether or not such a thing is possible, it's unknown... and obviously the ends don't justify the means)

Or he was just a power hungry dick.

While I am not too active on this site I would count myself as one libertarian who takes it to that extreme.

In regards to the OP I don't believe there are strong arguments from a libertarian perspective against market anarchy (I like to put that qualifier on there since most people think of anarchy only as a leftist/socialist movement even though there are capitalist anarchists like myself).

If there were I would be a minarchist too, but I can think of a few of the common fallacious arguments which usually are an appeal to fear (Ayn Rand's argument against free market anarchy is essentially fear based as she did not believe that people would make voluntary arrangements for the defense of private property in the absence of a state ... don't get me wrong I love most of her work but her casual dismissal of market anarchy was not well constructed).

Having presented market anarchism or anarcho-capitalism to a number of minarchist liberatrians I can definately say that they have been by far the most receptive to the idea. I can only count maybe one or two converts in my experience, but most are at the very least willing to entertain the idea. The only time I get outright rejection of the idea is when people confuse it for socialist/communist anarchism.

When you think about it there is something inherently irrational about libertarian philosophies like Objectivism and other forms of minarchism which trumpet the freedom , nonviolence and autonomy of individuals while arguing for a coercive and collectivist monopoly of force like government which is "needed" to protect us and our property from harm. Even if you could keep government small (which is impossible since there is no incentive for it to remain small, and thousands of years worth of attempts to restrain government have been a complete failure) it would still remain a coercive organization which violently extracts wealth in a given geographic region. If it was truly a voluntary organization as Constitutionalists and supporters of social contracts suggest then it would cease to be a government and become a security company, but that is not the case.

By definition government holds a monopoly on force and violently runs out competing agencies that would take its place by providing a better service for less as we see is the case in every other part of the market. It is as absurd as McDonalds going around and shutting down all restaurants that are not McDonalds in order to have a monopoly on the restaurant industry. No one would stand for that behavior, but we make an exception for government precisely because it is all we have ever known and we all average at least 12 years or more in schools made by the government for training loyals subjects to be at the government's disposal.

Most libertarians realize this, but they can't bring themselves to take the next logical step ... which trust me is hard and it took me years for me to finally be comfortable announcing the fact that I am an anarchist. It is a lot like the atheist/religious arguments where in this case minarchist libertarians would be agnostics to the atheist anarchist ... the agnostic is about 90% of the way there, but taking that final step can have serious consequences ... even more so for anarchists than atheists. I never lost a friend or even got into any serious arguments when I became an atheist, but I have since been in many heated arguments since I came out as an anarchist while losing friends in the process too. I would imagine that there are far more market anarchists out there than we would tend to expect, but many are just not outspoken or willing to self identify as one. There are also plenty who through no fault of their own remain ignorant ... the members of my campus libertarian club had never heard of anarcho capitalism before I introduced them to the concept.

That was all longer than I expected, but the basic point is that libertarians don't have strong arguments against market anarchism precisely because they share 99% of the same views as market anarchists, and they would probably be willing to identify as anarcho capitalists if not for ignorance or half hearted and absurd arguments like "who will make the roads." Even Ayn Rand who made a successful career out of being a very prolific libertarian author only had about a paragraph or two as a response to anarcho capitalism (which was itself just a fallacy of an appeal to fear mostly).

As a final note ... if anyone is aware of a more complete argument that Rand made against market anarchism then I would like to hear about it and read it as I have only read about half of her works, and I could only find a few paragraphs in a Q and A book on the subject.

I don't think they need to be mutually exclusive.  It could be that his hubris, with the observation of human nature, led Lenin to be Lenin politically.