Here’s the church’s teaching on the death penalty. It’s clear. While the death penalty is not totally excluded, the church teaches that, in practice there’s no need for it. Just because it’s not totally excluded doesn’t mean you can be in favor of it.

Assuming that the guilty party’s identity and responsibility have been fully determined, 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.
If, however, non-lethal means are sufficient to defend and protect people‘s safety from the aggressor, authority will limit itself to such means, as these are more in keeping with the concrete conditions of the common good and more in conformity with the dignity of the human person.

Today, in fact, as a consequence of the possibilities which the state has for effectively preventing crime, by rendering one who has committed an offense incapable of doing harm – without definitely taking away from him the possibility of redeeming himself – the cases in which the execution of the offender is an absolute necessity are very rare, if not practically nonexistent. (CCC, 2267)

The new evangelization calls for followers of Christ who are unconditionally pro-life: who will proclaim, celebrate and serve the Gospel of Life in every situation. A sign of hope is the increasing recognition that the dignity of human life must never be taken away, even in the case of someone who has done great evil. Modern society has the means of protecting itself, without definitively denying criminals the chance to reform. I renew the appeal I made most recently at Christmas for a consensus to end the death penalty, which is both cruel and unnecessary. (Pope John Paul II, Mass in St. Louis, MO, January 27, 1999)