I would forgive the murderer too eventually but only because of the Dilemma of Determinism. Free will doesn't truly exist. So basically what we become depends on what vagina we pop out of. I could have just as easily become that murderer in a different life and there's nothing unique about the fact that I didn't. It's all chance.

This concept is more intimate than child birth or military experience. ....when unexpected violence rips into our lives normal personal power or control is shattered. ....preachers are brainwashing some believers into contrived "forgiveness" blather. ...but for disciplined victims regaining control over revenge feelings and a myriad of other nightmarish daytime anguish, true forgiveness is internal not "given" to perpetrators but to our violated selves healing our wounded minds/bodies

I wouldn't and there fools

Well... in my opinion the whole "justice" system is generally messed up.
About forgiveness - essentially I do not think you have another choice but to forgive, or let go. Anger, hatred, revenge - they will not bring the beloved one back. Up till one point they serve to mitigate the pain of the loss, but after that - they just harm more and should be let go.
I can forgive, and have forgiven. And I would not seek revenge, provided the chance to get it. It will help nobody, nor me, nor the deceased.
And it has nothing to do with Christianity - it is just a general act of humanity. And at least within my personal system of believes, I place forgiveness as one of the three core virtues.

I can see a few possibilities for why they do it. I doubt it is ever because of concern over their christianity to any great extent. I suspect in capital crime cases the motive may be to make sure they don't leave a glaring t uncrossed when they trundle off to meet their maker in the great by and by. A few may even be aware enough to realize there could have been an error and they don't want to carry any blame for that. Still some may see it as part of the process, "Okay, le's get on up there and fergive the sumbitch so's we c'n get on with it." I guess you could say it is all part of the closure process, but I have no idea how one could legitimately justify that position. I suspect the real purpose for most is quite reasonably that it is not healthy to carry anger/hate overly long.

I think that it’s better to get that kind of anger and hatred out of your psyche before it metastasizes into something more virulent. If religion is what you have to use, ok. If all you can do is wish the guy a speedy trip to hell, ok. Frankly, I wouldn’t want to see anyone executed. Not that they don’t deserve it, I just don’t want to subject myself to the horror of seeing someone killed. I’ll find another means of consolation.

That’s all fine and well for the victim’s family. If it gives them release. However, if a convicted murderer killed a family member, I’d want a law stating the victim’s family gets to choose punishment. I vote the sentence to be: a live medical test subject or a live crash test dummy. This way the murderer is giving back to the community and I then can feel better, and maybe have a sense of forgiveness.

Forgiveness, properly done, is never about the one you forgive. It's for yourself.

The old saying is that not forgiving is like drinking poison and expecting the other person to die. Your bad feelings don't harm them at all. You forgive them for you, to take that load off your heart and mind. Finding forgiveness is hard, and sometimes it takes work, but it is necessary for mental health and inner peace.

Probably they say "I forgive him / her." more for themselves than for the murderer.

I don't enjoy watching it and avoid watching it