Active shooter in NZ

[WinterHold]

1-It ceases and stops reasons for revenge (the victim's family/people will have no justifiable reason to keep on killing to "avenge the fallen".

But capital punishment itself is an act of revenge.  It must be, as it serves no other purpose.
 

And what's wrong with an act of revenge based on the true, and just bases and cause?
If somebody killed my mom; he/she deserves to die just like she died; they deserve to suffer the same way she suffered. That's innate capacity for humanity; even countries do it in a more extreme way in wars -like the terrorist bombing of Dresden in WW2 and the invention of nuclear weapons-.
It's not just natural; it's a cure for the soul of the victim from negative thoughts that would turn -sooner or later- into a vengeance spree.

2-It is very just to treat an eye for an eye.

Then why don't we punish thieves by stealing from them, or arsonists by setting their homes on fire?

You should "return the money stolen" to the victim, so that is the taking -stealing- back what they stole.
The hand cutting is the prevention penalty. If losing a hand is the price of stealing, a thieve will think twice.

3-Society -with its rich and poor- will think twice -if not thrice- before the commit of murder

Really?  They haven't done that so far.  If you have evidence that capital punishment is a deterrent, do please trot it out.

Many reasons can make the killer don't fear death, including psychological state, pure ignorance, pure evil, pure sense of sacrifice, humans are known to fight in war for example knowing that they will probably get killed. The countries or places with a low homicide rates are usually wealthy, stable and prosperous. It is not lack of "deterrence" that is the sole father of killers, neither are these societies have low murder rates because capital punishment does not exist in their systems.

The father of killers is poverty, ignorance, and will to avenge somebody. The more you cause that, the more you give birth to killers without fear of death, some of them are even born thousands of years after the crime. 

But you need to take vengeance for the blood of the victims to turn the fire from spreading. Kill the killer and that fire is put down. Keep him alive, and you'll keep that fire lit for thousands of years even.