2263 | The legitimate defense of persons and societies is not an exception to the prohibition against the murder of the innocent that constitutes intentional killing. “The act of self-defense can have a double effect: the preservation of one’s own life; and the killing of the aggressor. . . . The one is intended, the other is not.”

2264 | Love toward oneself remains a fundamental principle of morality. Therefore it is legitimate to insist on respect for one’s own right to life. Someone who defends his life is not guilty of murder even if he is forced to deal his aggressor a lethal blow:

If a man in self-defense uses more than necessary violence, it will be unlawful: whereas if he repels force with moderation, his defense will be lawful. . . . Nor is it necessary for salvation that a man omit the act of moderate self-defense to avoid killing the other man, since one is bound to take more care of one’s own life than of another’s.

2265 | Legitimate defense can be not only a right but a grave duty for one who is responsible for the lives of others. The defense of the common good requires that an unjust aggressor be rendered unable to cause harm. For this reason, those who legitimately hold authority also have the right to use arms to repel aggressors against the civil community entrusted to their responsibility.

2266 | The efforts of the state to curb the spread of behavior harmful to people’s rights and to the basic rules of civil society correspond to the requirement of safeguarding the common good. Legitimate public authority has the right and duty to inflict punishment proportionate to the gravity of the offense. Punishment has the primary aim of redressing the disorder introduced by the offense. When it is willingly accepted by the guilty party, it assumes the value of expiation. Punishment then, in addition to defending public order and protecting people’s safety, has a medicinal purpose: as far as possible, it must contribute to the correction of the guilty party.

2267 | Recourse to the death penalty on the part of legitimate authority, following a fair trial, was long considered an appropriate response to the gravity of certain crimes and an acceptable, albeit extreme, means of safeguarding the common good.

Excerpts from Catechism of the Catholic Church, 2nd Edition
Part 3 – Life in Christ
Section 2 – Then Ten Commandments
Chapter 2 – You Shall Love Your Neighbor As Yourself
Article 5 – The Fifth Commandment