The Catholic Church's stance on the death penalty, as on many other issues, is not static. Cardinal Ratzinger, known as a conservative scholar (which earned him applause from conservatives and criticism from progressives), issued his understanding of doctrine in the text quoted by SupportiveDante almost 20 years ago. It is noteworthy that he does not make much of an argument — he is making a dogmatic statement: "Not all moral issues have the same moral weight as abortion and euthanasia." Period. No reason given; the text continues with examples.
Ratzinger's statement is not a full embrace of the death penalty and tries to keep all options open: "There may be a legitimate diversity of opinion even among Catholics about [...] applying the death penalty." Or there may not be! He is not saying that there is legitimate diversity, or that the diversity is legitimate. He is certainly not saying that a good Catholic couldn't be against the death penalty.
Times are changing, and the changing times brought a less conservative man to the top of the Church, Pope Francis.
He laid out a very different guidance regarding the death penalty in an address to the Pontifical Council for Promoting the New Evangelization. Francis starts with quoting a key section from the Catechism:
The whole concern of doctrine and its teaching must be directed to the love that never ends. Whether something is proposed for belief, for hope or for action, the love of our Lord must always be made accessible, so that anyone can see that all the works of perfect Christian virtue spring from love and have no other objective than to arrive at love.
This is a clear emphasis on what is at the center of Christian teachings, including the Catholic: Love. It is "along these same lines" that Francis turns to the death penalty.
We must take into account, he says, "the change in the awareness of the Christian people which rejects an attitude of complacency before a punishment deeply injurious of human dignity." He continues:
It must be clearly stated that the death penalty is an inhumane measure that, regardless of how it is carried out, abases human dignity. It is per se contrary to the Gospel, because it entails the willful suppression of a human life that never ceases to be sacred in the eyes of its Creator and of which – ultimately – only God is the true judge and guarantor.
That is a pretty apodictic statement: "It is per se contrary to the Gospel." But Francis, in contrast to his predecessor, does not simply issue a dogmatic statement — he gives us the reasons: By willfully killing a human we are usurping God's role, ending a sacred life.
With respect to different earlier teachings, Francis says:
Let us take responsibility for the past and recognize that the imposition of the death penalty was dictated by a mentality more legalistic than Christian. [...] Here we are not in any way contradicting past teaching, for the defence of the dignity of human life from the first moment of conception to natural death has been taught by the Church consistently and authoritatively.
The discourse ends thusly:
It is necessary, therefore, to reaffirm that no matter how serious the crime that has been committed, the death penalty is inadmissible because it is an attack on the inviolability and the dignity of the person.
Under his guidance, the Catholic catechism, which before saw the death penalty as a legitimate means of last resort, was amended in 2018 to include this quote in paragraph 2267.
Concluding, and coming back to your answer: Pope Francis, an authoritative source for opinions of the Catholic Church, clearly laid out the arguments against such a double standard. Those who did or do uphold it, like Cardinal Ratzinger, did not or do not have good arguments.