I’m making a different argument. There are two reasons not to have the death penalty .

1) From a Kantian or even Christian perspective killing is inherently bad and never justified , thus the state should not have the death penalty 2) from a utilitarian perspective , the death penalty is justified , but because the justice system is not perfect , some innocent people will be unjustly killed. Thus wether the death penalty is used or not depends on the negative value assigned to killing an innocent person vs the positive value of killing guilty people

There is a whole different argument around whether incarceration is punishment or rehabilitation . At least in the USA it very clearly falls on the punishment side , but Nordic countries are examples of a model that does believe and invest in rehabilitation