You need to hear about this really good book. its called The Catechism of the Catholic Church, and it addresses thisvery issue:
2267 Assuming the guilty party’s identity and reponsibility have been fully determined, the traditional teaching of the Church does not exclude recourse to the death peanlty, if this is the only possible way of effectively defending human lives against the unjust aggressor.
If, however non-lethal meansare sufficient to defend and protect people’s safetyfrom the aggressor, authority will limit itself to such means, as these are more in keeping with the concrete conditions of the common goodand more in conformity with the dignity of the human person.
Today, in fact, as a consequence of the possibilitieswhich the state has for effectively preventing crime, by rendering one who has committed an offense incapable of doing harm—without definitively 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 non-existent"
So really, I’m gonna have to disagree with you here.