Yesterday Bryan Caplan asked:

What’s wrong with revenge?  To be more specific: Suppose X is the most severe morally acceptable punishment for act Y committed by person Z. Suppose that the government fails to do anything about Y. What’s wrong if a person personally affected by act Y does X to Z?

In the comments, Matt C looks to bias: 

[Compared to public revenge,] personal revenge is too likely to get the wrong guy, and personal revenge is too likely to be excessive.

Acad Ronin looks to feuds:

"[The rule of law is] the transfer of the duty of revenge to the Queen. It’s the officers of the Crown avenging a man’s murder, not the man’s father or the family. Without law what you have is feud, tangling between themselves, and murder repaying murder down the generations. As we have here. But if the Queen’s Officers can be relied on to take revenge for a killing, then the feuding must stop because if you feud against the Queen, it’s high treason. That’s all. That’s all that happens in a law-abiding country: the dead man’s family know that the Crown will carry their feud for them. Without it you have bloody chaos."
Chisolm, P.F. 1994. A Famine of Horses. New York: Walker and Co.

If the feud problem itself results from biases, these could be the same explanation.