While you may see no good in it, as do I, in fact, those who commit the crimes have to have some motive. It's like saying "I hate this food" but then someone else likes it. It's a difference in opinion, really, and while most may believe it to be wrong, it is not entirely so, as, out of 6 billion people (nearing 7, I believe) there is bound to be a select few who have opposing opinions and, while we say wrong, they say right.
Much like the difference in opinion Light and the police have (getting back to the subject). While Light believes he is justice, L believes that he is injustice.
That's what I mean by nothing is always entirely right or wrong.
When it comes to justice, it's a territorial issue.
The cops, the law, the judges, the state; in a 'modern' society those are (supposedly) the sole propietors and dispensors of justice. When a vigilante or some other party outside that order appears, someone who dispenses justice on his own accord, it does not matter what the vigilante believes or if his brand of 'justice' is the same as the cops' or not. It does not matter if the vigilante acts for justice at all or for his own selfish needs. Conflict is inevitable, b'cos he is outside the structure and control of the police, yet he still takes their role. That his methods are more efficient than the police, it is bound to make the police feel even more threatened by his mere existance. For one man to become the 'new' police, the 'new' state, the one who ultimately decides who lives and who dies, that is a threat to the modern society on so many different levels.
And there are absolute rights and wrongs in this world, things dictated by nature, things dictated by heaven, etc.