It has such a bad reputation because it is as unworkable a system as pure communism. Both, actually, have nonexistence of the state as an end goal. Where communism breaks down is that human nature will never allow dissolution of the dictatorship of the proletariat. You can call it socialism if you like, but it's really a dictatorship where the centralized power is held by a select few. You start with a revolution, transition to a dictatorship of the proletariat, and stop. Human nature takes over. Anarchy is the same way. You have a revolution followed by a transition to chaos, out of which will form a spontaneous order of free individuals in autonomous communities, operating on principles of mutual aid, voluntary association, and direct action. In reality what you would get is a dictatorship of the strong, see Somalia for an example. Warlords imposing their will upon others with nobody to challenge them except other warlords.
That's the practical opposition to anarchism, namely that it assumes, in the absence of law, that people won't riot or take things by force. On a more basic level it negates the theory of the rule of law as being unnecessary, and the rule of law is the backbone of our civilization. When people join together to form societies disputes are inevitable, both in physical terms and contractural terms. People will fight. And people will lie, cheat, and steal. Governments are put into place with the purpose of peacefully settling these disputes. Whether it's arresting and imprisoning the man who shot your brother or forcing a company to deliver the services you've paid them for, a system of settling disputes peacefully is required. And part of implementing such a system is that the citizens RECOGNIZE the authority of those who maintain the laws. Anarchism, depending on the flavor, does not recognize anything beyond a nebulous social authority enacted at the lowest community level. Hence there is no real rule of law, but rather a frontier justice mentality that cannot truly protect the rights we consider our birthrights. And the protection of those rights is the main reason we have a government in the first place. Hence an anarchist state is one where our rights are not protected, and most people have a negative view on such a society.
I myself am a Libertarian, and probably closer to an anarchist than most. But I realize that the world is not perfect, human nature does exist, and that governments are necessary. Their actions should be minimized and closely controlled, but within the scope of the authority we grant them they do need to be able to exercise that authority. I know there are subclasses of anarchy, but as a general discussion this is how I see it.
Edit (for Joe)-
That article has numerous flaws with its logic. I'll spell them out.
1) Tu Quoque Fallacy
"It is not enough to demonstrate that a state of private-property anarchy could degenerate into ceaseless war, where no single group is strong enough to subjugate all challengers, and hence no one can establish “order.” After all, communities living under a State degenerate into civil war all the time.
Ahh, the old "you too" fallacy. That communities living under a state CAN degenerate into civil war does not impact the LIKELIHOOD of the aforementioned degeneration happening. It simply points out that it is POSSIBLE with a state. This does not impact the premises or the core conclusion, namely that it is more likely to happen in the absence of the state, and hence must be discarded.
2) Ad Hominem attack
"For the warlord objection to work, the statist..."
If you look at and understand the Nolan chart you can classify anarchists as extreme libertarians, occupying the absolute pinnacle. Even if you throw in some of the other flavors, such as anarcho-capitalists and anarcho-socialists you're still only covering between 3-5%. Whereas statists would comprise maybe 20% on the top end. Calling everyone who disagrees with you on this point a statist isn't just offensive, it also shows a fundamental misunderstanding of the terms being used.
3) Straw man fallacy
"For the warlord objection to work, the statist would need to argue that a given community would remain lawful under a government, but that the same community would break down into continuous warfare if all legal and military services were privatized."
Be very, very careful when you let the opposing side try to frame the argument you wish to make. If they tell us what "statists" must do to make their argument then chances are that argument will be subtly altered and easily brushed aside. Which is the case here. What we can argue is NOT that a given community would remain lawful, but rather that the unlawful elements would be ABLE and LIKELY to take over. I do not need to look far for examples here, Cabrini Green in Chicago, The Marcy Projects in New York, or pretty much the entire county of Los Angeles. Here we have a situation where even though 90% of the population is law abiding the lack of law enforcement results in a dictatorship of the strong. The gangs take over, not because the community doesn't respect the law but because a small criminal element of the community doesn't respect the law and there is no recourse for the law abiding other than to form gangs of their own. Which basically degenerates into the competing warlord scenario.
4) Appeal to ignorance
"The popular case of Somalia, therefore, helps neither side.[i] It is true that Rothbardians should be somewhat disturbed that the respect for non-aggression is apparently too rare in Somalia to foster the spontaneous emergence of a totally free market community. But by the same token, the respect for “the law” was also too weak to allow the original Somali government to maintain order."
Respect for "The Law" is not what keeps those who disrespect the law from taking over, it is respect for the ENFORCEMENT of the law. Which was non-existent in Somalia. That a law exists means nothing if it is not enforced. The situation in Somalia is analagous to the gang situations in the inner cities. A state incapable of enforcing its own laws is the same as no state at all. The attempt to equate both the positive and negative premise, and then conclude that no conclusion is possible, is an appeal to ignorance since the positive premise has not been disproven.
I would be interested in hearing how a warlord would not actually be considered a privatized provider of legal and military services. They seem to be closely related. A warlord dispenses justice, as he sees fit. He also wages war for the benefit of himself and his "community". How is that not a private army or justice system, as called for in this article?