Discussion on the issue of Catholic teaching on capital punishment is reoccurring (here and here). What the Catechism says about this is quite straightforward and easy to understand.

Assuming that the guilty party's identity and responsibility have been fully determined, the traditional teaching of the Church does not exclude recourse to the death penalty, if this is the only possible way of effectively defending human lives against the unjust aggressor.

If, however, non-lethal means are sufficient to defend and protect people's safety from the aggressor, authority will limit itself to such means, as these are more in keeping with the concrete conditions of the common good and more in conformity to the dignity of the human person.

Today, in fact, as a consequence of the possibilities which the state has for effectively preventing crime, by rendering one who has committed an offense incapable of doing harm – without definitely 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 nonexistent".

Despite this clarity, there is practical dissent to this teaching. The argument that leads to dissent runs along lines like this:

"The Church does not teach that capital punishment is always wrong — prudence is required to discern when it is permitted and when it is not. So I may legitimately disagree with the prudential judgement of other Catholics, and even the Pope."

And that is an ambiguous argument; the first sentence is certainly true, but the second sentence has both a true and a false sense.

To support the argument, a quote from the Pope (when he was a cardinal) is often supplied:

Not all moral issues have the same moral weight as abortion and euthanasia. For example, if a Catholic were to be at odds with the Holy Father on the application of capital punishment or on the decision to wage war, he would not for that reason be considered unworthy to present himself to receive Holy Communion. While the Church exhorts civil authorities to seek peace, not war, and to exercise discretion and mercy in imposing punishment on criminals, it may still be permissible to take up arms to repel an aggressor or to have recourse to capital punishment. There may be a legitimate diversity of opinion even among Catholics about waging war and applying the death penalty, but not however with regard to abortion and euthanasia.

The part that seems to spring out is: "There may be a legitimate diversity of opinion..". But it does not logically follow from this that all different opinions are legitimate. The quote does not imply that. It says that if you disagree with the Pope on whether some particular abortion can be justified, then — without any further investigation of the cirucmstances — I can automatically conclude that you are wrong. If you disagree with the Pope on whether some particular application of capital punishment is justifiable, then I can't conclude automatically that you are wrong — I must look at the circumstances and on how prudence was applied before I might conclude that.

Nor does it follow from the quote that we are free to decide the grounds on which a prudential judgement can be made. Church teaching defines those grounds for us ("if this is the only possible way of effectively defending human lives against the unjust aggressor").

To decide based on other grounds is not allowable.