I assume you are referring to punishment. When you commit a crime and are found guilty, you are sentenced a harm (fine, jail time, and, in some cases, death). It may be true that this system, from an evolutionary biological perspective, probably has its roots in our feelings of fairness and empathy being violated, thus producing feelings of anger and a desire to harm the transgressing individual. However, law also allows for societies to work and live together in a more uniform way, so there is a lot more to law and justice than those feelings. — Chany

If you are indicating that 'feelings of anger and a desire to harm' (I prefer the description malice or ill-will, but it is pretty much the same thing) are associated with an act of vengeance but not an act of justice, then I agree with you.

However eye for an eye is evidently proportionate to an offense, thus according to you, it falls under justice. Yet, generally speaking, this philosophy of justice is considered immoral. — TheMadFool

I think the Bible passage(s) that refer to 'an eye for an eye' could be construed as an attempt to prevent redress from going to far ie no more than an eye for an eye. I don't think they are meant to be taken literally.