One of the libertarian arguments against government boils down to one simple question. Do you feel strongly enough about an issue that you are willing to have me killed or imprisoned to get your way?
Illustrative example, you believe in a law against fences higher than six feet. Suppose I build an eight foot fence around my property. A likely progression of action over the long term might be that I would receive a warning to tear down my fence, eventually I would be fined for refusing to tear down my fence, after that I might be arrested and jailed for refusing to pay the fine, and it is certainly within the realm of possibility that I could be killed by the police if I resist being arrested. This is an extreme example, but the net result of you passing a law against my choice of fence is that I could be killed for building a fence that you disapprove of.
In a nutshell, this is why libertarians disapprove so strongly of ceding power to a government. Since government is, by definition, a legal monopoly on the use of force, their only recourse in the event of non-compliance is the threat or use of force. Refuse to obey use and we will initiate force against you. It may take some time and there may be intermediate steps, but as the above example illustrates, eventually, if you refuse to comply with their dictates, government agents will either have to ignore your disobedience or use force against you.
So why did Eric Garner die? I am not a strong critic of the police, although I do have concerns which tend to be specific rather than institutional. They are generally doing their jobs the best that they can. In this case it appears that a combination of Garner's frustration at being arrested, his health conditions, and use by the police of a choke-hold to subdue him are what resulted in his death. I don't know any details about the specific hold used on Garner but I do know that some types of choke hold are banned by many police departments, including the NYPD, specifically because they can result in death. Without knowing any facts other than what has been reported in the media I tend to lean towards the conclusion that the NYPD probably bears the most liability in this death, but that Garner contributed by resisting arrest.
A more important question in my mind is why the police were arresting Garner to begin with. He was selling "loosies" on a street corner. New York City has a per pack tax on cigarettes of almost six dollars. Per pack. Not per carton, per pack. A pack of cigarettes costs about $14 in the city. So Garner was apparently selling cigarettes bought out of state for $.50 each. $10 a pack. This is illegal because the City doesn't get to collect their pound of flesh.
Eric Garner is now dead because the State has no way to enforce their rules except through the use of force. He broke a petty, bureaucratic, controlling rule and he died because that is how they ensure compliance.
The only way to prevent the death of the next Eric Garner is to reduce the reach of the government apparatus. If selling cigarettes on a street corner isn't illegal, then there is no reason for the police to be assaulting you on that corner. Reduce the power of government, reduce the "legal" reasons for them to assault you.
Question of the day: If self defense is the prerogative of a free man, but initiation of the use of force is illegitimate, why do we grant that power to the state?