The problem is that the Catechism disagrees with itself; what is said in 2267 does not coincide with what is said in 2260 and 2266.
It isn’t so subjective that we should be unsure of what it is. Specifically, Punishment is proportionate to sin in point of severity, both in Divine and in human judgments. (Aquinas ST I/II,87)
The Church recognizes four valid objectives of punishment: retribution, protection, deterrence, and rehabilitation. Retribution - demanded by justice - is the primary objective; the others, including protection, are all secondary. In placing the limits it does on the use of capital punishment, 2267 refers solely to protection and ignores retribution and so the moral concept of justice is severed from the punishment. Under a defending society standard, the injury suffered by the murder victim is no longer relevant to the punishment inflicted. Executions can be justified only if they are able to prevent future harm by the murderer. It is the likelihood of future crime that is punished, not the crime already committed, which you have to admit is fairly bizarre: a person may be executed to prevent the crime he could not be executed for committing.
You define what the Church obliges as “an eye for an eye.” The Church defines punishment that is commensurate with the severity of the sin as justice.
Ender