The Catechism (#2267) says, “The traditional teaching of the Church does not exclude recourse to the death penalty, if this is the only possible way of effectively defending human lives against the unjust aggressor.” While in theory the state (civil government) has the right to impose capital punishment, it is neither an absolute nor an unrestricted right. Just as there are legitimate limitations on free speech (for example, it is immoral and illegal to commit perjury), there are limitations on the moral use of the death penalty.
If non-lethal means are sufficient to defend and protect the common good and public safety, then the necessity of capital punishment begins to diminish greatly. Today, in view of more effective crime prevention, more secure prisons, and the technology to monitor movements of released prisoners, the justifications for execution (in the words of Pope John Paul II in Evangelium Vitae, Gospel of Life, 1995) “are very rare, if not practically nonexistent.”
Therefore, without denying in principle the right of the state to impose the death penalty, the moral justifications may not always be present. Another problem besides the debate on whether or not capital punishment is truly a deterrent is the inequitable application in many instances. Each state in the US decides for itself whether or not it will execute certain criminals and which crimes warrant this extreme punishment, so it is not just the crime itself, but also where it took place that often determines if you are subject to the death penalty. Often, if you are a celebrity or someone with vast financial resources, you can hire an expensive and qualified legal team to defend you, whereas the poor person gets a public defender, who may be extremely qualified but is also usually overworked.
Since there is no universal application (same crime, same punishment), the previous pope and the Catechism seem to dissuade public opinion from capital punishment. It is not condemned as never being applicable; rather, the criteria for it do not seem to be present at this point and time in history. The prudential judgment of whether or not the moral principles have been fulfilled to make it a morally permissible act (war or death penalty) rests with those in authority who are authorized to care for the common good. There may be disagreement even among or with some church leaders in terms of practical or specific implementation or application as long as the general principles are respected and upheld.