I noticed that in today’s arguments about the death penalty, people talk past each other with stuff like economics and deterrence; nobody really mentions its primary purpose anymore, as put forth by the Church’s moral theology and St. Thomas Aquinas.
In answer to the question, the death penalty accomplishes, first and foremost, retribution. That is, its primary purpose is punishment, not deterrence, not rehabilitation. It does not bring the victim back, but that’s not its purpose. It does not even bring closure to the survivors, but that’s not its purpose either. The death penalty, just like any other sentence, has as its primary objective the application of justice, that is, for any crime, a proportionate punishment must always be inflicted on the offender.
Comparing a murder to a pit bull does no good because a pit bull is not being punished; it is put down to remove a danger. While the death penalty also removes a danger to society, this is merely secondary to the primary purpose. This comparison undermines the dignity of the offender, which is what allows him to pay for his crime (i.e. it is precisely because the offender has human dignity that he is capable of paying for his crime, even with his life).
This is why the Church has never objected to the death penalty as an instrinsic evil for she has always viewed it as a just punishment for certain crimes.