From my perspective, I've found that many against promoting rehabilitation (at least for less heinous crimes) tend to see prison as a day at the park.

Essentially, they're trapped in a prison in the form of low income or poverty where significant portions of their time must be spent working. They don't understand how a prisoner could potentially or at least perceptually be better off than them: consistent housing provided, guaranteed food, medical treatment, time for education and growth. When you have such gaps with economic inequality in a society where for those on the lower end of the spectrum combined with some misconception of prison life, prison can actually seem better, you have many who tend to promote punishment over rehabilitation.

"Someone did something society deemed as negative and they're rewarded, I did what society said was positive and seem to be punished relative to those acted negatively. I struggle to survive and work constantly while this person leisures (albeit with limited freedom) and studies."

So as you coined it, probably spite.

Or, a sense of justice. A powerful emotion in people.

Who know how many more criminals there might be, if punishment was off the table? Recidivism doesn't count that. So there's that social pressure too.

Its pretty easy to figure out 'why punishment', if you try.

Who knows how many fewer criminals there might be, if social safety nets, providing for people's basic needs of food, shelter, health care and education?

How do you cure homelessness? You provide homes.

How do you deal with mental and physical illness? You provide health care.

How do you give people are path forwards? You provide education.

All of these things are what our societies are for. To carry on about "law and order" and even the "rule of law" without also quoting the part about "promote the general welfare" is to completely miss the purpose.

We should certainly provide all of those things. But even homeless people, ill people, people with no direction in life can and should avoid committing crimes.

It's pretty easy to figure out 'why we shouldn't focus on revenge', if you try.

edit: I may be guilty of not listening to what you're actually saying. If you're saying there is something in the core of people that is delighted by revenge, therefore the current system, I agree. If you are saying that justifies a focus on punishment, I disagree.

Not necessary to color everything with the worst adjective at hand. A sense of 'justice' is a thing. Calling it 'revenge' devalues it, and implies a personal component that isn't present.

Justice is the sense that good action will be rewarded, and bad actions will come to a bad end. Not "I'm gonna kill anybody that crosses me!" They are very different, and its not useful discussing this if that is not clear.

How do we know punishment is not a deterrent to crime?

If there was no punishment for committing crimes, do you think the amount of crime would remain approximately the same and is there any good evidence for that?

I think it's probably not a deterrent to some crimes, but a deterrent to others. Probably there are lots of people who don't shoplift, e.g., out of fear of the consequences of getting caught. (Obviously there are plenty who would not steal regardless; and plenty who steal anyway). Most studies I've seen on deterrence focus on the most serious crimes like murder and rape.

we can debate if that's logically or morally right, but there's no doubt spite and hate are powerful motivators