Today, the reverse is true. Only the most serious crimes qualify for the death penalty. Therefore, the need to show mercy and not execute someone, even for a grave crime if another alternative exists that safeguards society. The fact that justice is served is a given today. We do not execute thieves.
First, put it in a broader historical context. For the first millenia, the Church battled against infanticide. Killing or discarding unwanted newborns was far more prevelant among the gentiles of the ancient world than abortion. The Church still struggles with small pockets of this today (in South American there are still pockets that ritualistically bury deformed new borns alive).
By the 12th century or so, a stigma had at least started to take root. But still, abandonment remained a problem for several centures more. The Church battled this by offering mechanisms for anonymous abandonment (sort of a ‘lazy susan’ device at Church supported orphanages.
Similarly, it took us 1800 years to finally acknowledge the problem of slavery. 1900 years to make our ban on abortion absolute. 2000 years to question the death penalty.
From about 1869 forward, the Church has been pushing for a unified understanding of the inalienable rights of the human person. Multiple Popes laid groundwork, then it was reviewed and validated by the Second Vatican Council. This paved the groundwork for works like Evangelium Vitae. The teaching that we treasure each life as a unique creation of God, at “any stage” and in “any state” makes our absolute ban on abortion and euthanasia understandable.
But, if the belief is truly held, then the death penalty must only be used in the face of extraordinary societal risks. There is no evidence that the presence (or absense) of the penalty has a meaningful impact on societal risk. On the other hand, we do know that the penalty is neither even handed, or infallibly applied. So, you have cases of innocent (at least of their accused crimes) and defenseless people being put to death. This is wholly contrary to the point of the teaching.
The biggest flaw I see in this discussion is the seeming assumption that the death penalty can be considered in isolation. It isn’t isolated. We are either each a unique creation of God, infinitately loved, or not. Spiritual judgement is either God’s providence, or it is not. And we either value life at all stages and in any state, or not.
Do some horrible people deserve to die? Almost certainly. Whoever approved the use of white phosphor as a weapon in urban combat would make my list. But we aren’t going to kill all the ‘bad’ people, unless we want to be Nazi Germany or Stalin’s ‘utopia’. So we are going to have dangerous people incarcerated. With that in mind, or the data available comparing us to other nations, state to state, or even different periods, it is hard to see that the death penalty is desired for anything other than simple ‘vengence’. And an ‘eye for an eye’ is one of the few items from the Jewish Bible that Christ directly challenges in the New Testament.
Again, I understand people will disagree. My intensity is that I happen to think that our current pope is also correct about the perils of moral relativism. In the US we frequently show disdain for our ordinary, and only marginal deference for the Pope.