According to the average statist, "justice" involves preemptively hurting someone because their actions might possibly, theoretically hurt someone else in the future, maybe, according to someone else's opinion. Examples of this abound, but the issuing of speeding tickets is an excellent example. No victim, but you know, there could have been, perhaps, if all the stars aligned in the wrong order.
These statists also believe that "justice" involves hurting someone after the fact, when the crime is done and over and no further potential for harm remains. The hurt that will be put on the offender, by the way, will be charged to others, thereby victimizing uninvolved innocents in order to seek retribution against someone for their past sins. The most obvious example of this type of "justice" is incarceration.
Many (and possibly a majority) of those incarcerated never hurt anyone at all (such as those convicted of drug use, weapons charges, or vices) and thus fall under the preemptive harm problem, but even among those who actually harmed someone (through murder, rape, theft, etc.) there is the problem that the penalty comes after the fact. You can't un-murder or un-rape someone, but you can at least make some financial restitution to the victims of these crimes... You could, that is, if you weren't locked up. Instead of making restitution, these offenders are costing innocent people more money. Talk about a lose-lose proposition.
Ironically, the type of justice most opposed by the average statist is the only real kind of justice possible—terminating ongoing aggression. This is what armed citizens are able to do. Instead of letting a murder, rape, or robbery take place, armed citizens put a stop to it. They do this both by deterring the crime before it happens (who wants to get into a gunfight just to rob a convenience store?) and by using deadly force when required to STOP the attacker before he can complete his crime.
Justice isn't about using violence to counter perceived risk (such as harming people because of how fast they drive or what substances they choose to ingest) nor is it about seeking revenge for past actions. True justice is about stopping ongoing aggression in a manner which ends the harm being done to innocents. We don't need more cops, more prisons, or more laws—on the contrary, they only make things worse—we need more armed citizens who are willing and able to stop aggression in its tracks.
Why do statists oppose this kind of justice? It's simple really. If armed citizens started terminating ongoing acts of aggression, the statists would find themselves facing armed resistance every single time they attempted to engage in theft and redistribution or to impose their preferences on others. In other words, statists oppose true justice because it demands they abandon statism or face extermination. True justice isn't a component of statism; it is its very antithesis.