Retribution as understood under the Old Law ie. an eye for an eye, does not apply for Christians. As Cardinal Avery Dulles states in his First Things article…
*Retribution by the State has its limits because the State, unlike God, enjoys neither omniscience nor omnipotence. According to Christian faith, God “will render to every man according to his works” at the final judgment (Romans 2:6; cf. Matthew 16:27). Retribution by the State can only be a symbolic anticipation of God’s perfect justice.
For the symbolism to be authentic, the society must believe in the existence of a transcendent order of justice, which the State has an obligation to protect. This has been true in the past, but in our day the State is generally viewed simply as an instrument of the will of the governed. In this modern perspective, the death penalty expresses not the divine judgment on objective evil but rather the collective anger of the group. The retributive goal of punishment is misconstrued as a self-assertive act of vengeance. *
Eye for an eye is not about vengeance, it’s actually a restriction. The Lord is commanding the Israelites to limit the punishment to only the degree of the crime, hence eye for eye, not life for eye.
Yes, there can be a vengeance aspect to punishment, and this is not what the Church wants. But the retributive aspect in itself is moral and is in fact the prime purpose of punishment. It does apply to Christians, based both on Scripture and Tradition.
Scripture: Romans 13: 3 For rulers are not a terror to good conduct, but to bad. Would you have no fear of him who is in authority? Then do what is good, and you will receive his approval, 4 for he is God’s servant for your good. But if you do wrong, be afraid, for he does not bear the sword in vain; he is the servant of God to execute his wrath on the wrongdoer.
Tradition: Pope Pius XIIEven in the case of the death penalty the State does not dispose of the individual’s right to life. Rather public authority limits itself to depriving the offender of the good of life in expiation for his guilt, after he, through his crime, deprived himself of his own right to life.
Tradition: Council of TrentThe power of life and death is permitted to certain civil magistrates because theirs is the responsibility under law to punish the guilty and protect the innocent. Far from being guilty of breaking this commandment [Thy shall not kill], such an execution of justice is precisely an act of obedience to it. For the purpose of the law is to protect and foster human life. This purpose is fulfilled when the legitimate authority of the State is exercised by taking the guilty lives of those who have taken innocent lives.
All of these are from the Christian era and as you can see, the punishment of the guilty is paramount. Feel free to agree that states should not impose the death penalty for any reason, be it human frailty, the risk of a miscarriage of justice, current modern mindsets, or even just a simple opposition to the taking of another human life. It’s perfectly fine to oppose capital punishment on these grounds.
But the moment you state that retributive punishment is not Christian, or the death penalty is itself inherently immoral, then this is contrary to the timeless teaching of the Catholic Church, because the Church cannot change a teaching on morals.