The church has never taught that capital punishment is a form of self defense, and indeed the two categories have quite different objectives and requirements. The primary requirement for killing in self defense to be valid is that the killing not be intended or desired. For capital punishment, however, the death of the prisoner is the entire objective of the act. This is very likely why Pope Francis
said:
Nevertheless, the prerequisites of legitimate personal defence are not applicable in the social sphere without the risk of distortion. In fact, when the death penalty is applied, people are killed not for current acts of aggression, but for offences committed in the past. Moreover, it is applied to people whose capacity to cause harm is not current, but has already been neutralized, and who are deprived of their freedom.
Your claim does not accord what the church teaches:*“It is lawful to kill when fighting in a just war; when carrying out by order of the Supreme Authority a sentence of death in punishment of a crime; and, finally, in cases of necessary and lawful defense of one’s own life against an unjust aggressor.” *(Catechism of Pope St. Pius X)
That acting out of hatred is wrong is true of all punishment. This is nothing unique to capital punishment.*It is unlawful to desire vengeance considered as evil to the man who is to be punished, but it is praiseworthy to desire vengeance as a corrective of vice and for the good of justice; and to this the sensitive appetite can tend, in so far as it is moved thereto by the reason: and when revenge is taken in accordance with the order of judgment, it is God’s work, since he who has power to punish “is God’s minister,” as stated in Romans 13:4. *(Aquinas ST II-II 158, 1 ad 3)
It is surely true that circumstances influence a person’s behavior, but we should never believe that a person should not be held accountable for his actions, for that would strip him of his human dignity and reduce him to the level of beasts, who we do not hold morally accountable.*In not a few cases such external and internal factors may attenuate, to a greater or lesser degree, the person’s freedom and therefore his responsibility and guilt. But it is a truth of faith, also confirmed by our experience and reason, that the human person is free. This truth cannot be disregarded, in order to place the blame for individuals’ sins on external factors such as structures, systems or other people. Above all, this would be to deny the person’s dignity and freedom, which are manifested–even though in a negative and disastrous way also in this responsibility for sin committed. Hence there is nothing so personal and untransferable in each individual as merit for virtue or responsibility for sin. *(JPII, Reconciliatio et paenitentia)
Ender