I also like to add this statement from the link I cited:
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Indeed, the early Church (for example, in the writings of Clement of Rome [died 101 A.D.] and Justin Martyr [d. 165]) generally found taking human life to be incompatible with the gospel. Christians were not to participate in capital punishment. Later, after Christianity became the religion of the Roman Empire, opposition to the death penalty declined. Augustine recognized the death penalty as a means of deterring the wicked and protecting the innocent. In the Middle Ages, Thomas Aquinas reaffirmed this position.
The new Catechism of the Catholic Church reflects this tradition, stating that the death penalty is possible in cases of extreme gravity. However, the Catechism adds: “If bloodless means [that is, other than killing] are sufficient to defend human lives against an aggressor and to protect public order and the safety of persons, public authority should limit itself to such means, because they better correspond to the concrete conditions of the common good and are more in conformity to the dignity of the human person” (#2267). Clearly, then, the bishops’ opposition to the death penalty is in accord with universal Church teaching…**
Note the words, EXTREME GRAVITY.