"No human being has the right - under any circumstances - to initiate force against another human being, nor to threaten or delegate its initiation."
From the pages of The Libertarian Enterprise comes this:
"A libertarian is a person who believes that no one has the right, under any circumstances, to initiate force against another human being, or to advocate or delegate its initiation. Those who act consistently with this principle are libertarians, whether they realize it or not. Those who fail to act consistently with it are not libertarians, regardless of what they may claim."
- L. Neil Smith
Some people consider theft and fraud to also violate the ZAP as these are forms of force; they take from you what you have worked for with your own time and labor against your will or under false pretext. Can you see how "taxation" fits in here as well? Others insist that these are not physical force, so they do not violate the ZAP, even though they are still wrong. The ZAP is essential, but not sufficient.
Many, if not most, of the criticisms of libertarians I have read revolve around misinterpretations of the ZAP. Some critics argue that libertarians are pacifists. Others argue that one or more core concepts of "The State" are good or "necessary evils". Still others argue that libertarians will strike out and kill anyone who angers us using the excuse that the other person initiated force. On the other hand, anyone with a functional intellect can see and understand when force has been initiated. Pointing a gun at a person who is making an obscene gesture at you in traffic is initiating force. Carrying a gun in your holster is not initiating force, even if a hoplophobe sees it and has a panic attack. Taking a person's property from them while implying that there will be consequences if the person does not comply is initiating force. Asking for a donation is not. The critics just don't get it and are not thinking. They ignore the word "initiate" in almost all cases. Probably intentionally, since they have no other argument.
A libertarian may or may not be a member of the Libertarian Party, which usually strays far from libertarian principles and ignores the ZAP. This is the distinction between what is called a "big 'L' Libertarian" and a "small 'L' libertarian".
Then there are the anarchists and the minarchists. Both may consider themselves a type of libertarian. "Anarchy" means "no rulers". The definition of "anarchy" has been corrupted to be understood as "no rules; chaos". There is a big difference between "no rulers" and "no rules". "Minarchy" means "minimum rulers". Few people have ever heard of "minarchy" so the definition hasn't had a chance to be corrupted yet.
I have heard it argued that the word "libertarian" has been corrupted by obviously non-libertarians calling themselves a "libertarian". Actions speak louder than words. If someone acts like a socialist, then that person is a socialist. Some of them try to call themselves some sort of "hyphenated libertarian"; a "socialist-libertarian" or a "libertarian-leaning conservative". Don't buy what they are trying to sell you; it is contaminated.
Some people believe, as I do, that government is not necessary (or possible) within a true libertarian society. These are the "anarchists". Government. or the belief in it, is built upon coercion and theft: the people who live within its sphere must do what the government demands or some form of punishment will be forced upon them. Government takes money from the people by theft called "taxation". If it were not theft, there would be no punishment for not paying and it would be completely voluntary.
Some people believe in what is known as "minarchism". They think it is possible to have a tiny, weak government which will provide for regional defense, punish those who violate the ZAP, and maintain roadways within its sphere of influence. How will these functions be financed? How would the roadways be built without taking land from someone against their will? Minarchists are still statists. A statist is anyone who believes that "governing others is a legitimate human endeavor".
At the other end of the spectrum are the "authoritarians". Authoritarians are a worse subset of the "statists". Authoritarians are the people who normally seek "public office". They believe that people must be controlled. They believe in such concepts as "the public good", "social contracts", and "implied consent". Authoritarians do not believe you have the sense to run your own life, as they believe that people are weak and stupid. Yet they seek power over your life while demonstrating time and again that they are no more intelligent than you are. If people cannot be trusted to run their own lives, how can they be trusted to run the lives of others? Who knows what is best for you? Some person in a far away government office, or you?
Libertarians acknowledge that YOU own your life. They recognize that you know what is best for you, and that you can achieve your best without preying on anyone else. If you wish to live under the control of authoritarians, that is your decision, but you have no right to impose that on anyone else. Unfortunately this is where the conflict arises: authoritarians can not allow anyone to live unmolested. They invariably initiate force against people whose only crime is wishing to be left alone. Once that line has been crossed and force has been initiated, force may be used legitimately by libertarians in defense of their lives, liberty, and property. This is what the Declaration of Independence was all about. Ask yourself the "Shorty Dawkins questions": "Would the founding fathers be proud of the government and society of today? Do you think they would revolt again?"
Never mind that they messed it all up by establishing another government and dreaming up "authority" out of thin air (the only place the superstition of "authority" exists).