> "because I want the person to suffer" is not a valid reason to lock someone up.
It's one of the established reasons: deterrence, incapacitation, rehabilitation, and retribution. The following are all from Wikipedia:
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Deterrence is the use of punishment as a threat to deter people from offending.
Incapacitation in the context of sentencing philosophy refers to the effect of a sentence in terms of positively preventing (rather than merely deterring) future offending.
Rehabilitation is the re-integration into society of a convicted person and the main objective of modern penal policy.
Retributive justice is a theory of justice that considers punishment, if proportionate, to be the best response to crime. When an offender breaks the law, justice requires that they forfeit something in return.
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The U.S. certainly puts more weight to retribution - in my opinion, too much weight - while European justice systems are more interested in rehabilitation, sometimes being ridiculously naive.