If you look at legal theory, the actual reasons for punishment are a mixture of deterrence, prevention, rehabilitation and retribution.
It is certainly possible to question how well any of these goals are met, or even the overall framework. But it is useful to start with the reality of how folks talk about punishment in a criminal justice context.
Ref: search "purpose of criminal punishment" and pick one.
Your whole comment comes off as exceedingly arrogant. OP is pretty clearly talking about retribution, so calling this out as one of the "actual" reasons is condescending and a non-sequitur. Moreover, assuming that somebody will agree with you after Googling something implies the only source of the disagreement is another person's lack of knowledge - this is again exceedingly condescending.
It is certainly possible to question how well any of these goals are met, or even the overall framework. But it is useful to start with the reality of how folks talk about punishment in a criminal justice context.
Ref: search "purpose of criminal punishment" and pick one.