The Church is opposed to capital punishment in a different way than how it is opposed to abortion, euthanasia, contraception, embrionic stem cell research (of which in a moment) and gay "marriage". The above five (and also female priests, although they usually are not listed together with the first five) are intrisically wrong, -- there is no circumstance when these are allowable by exception. The first five are on the so-called non-negotiables list because thay are also political controversies which a Catholic MUST wholly and without exception oppose.
The Capital punishment is opposed not in principle but because in advanced societies there is normally an aediquate prison system that can hold dangerous criminals forever. Since it is not necessary to kill a criminal to protect form further crime, the Church prefers his life to be spared. However, in the past where, prison escapes were possible, or today where the needs of self-defense cannot be met without killing the criminal, the Church does not oppose the death penalty. Consequently, a Catholic MAY suppor the deat hpenalty even in the US or some other advanced country on the grounds that in fact, the American justice system does NOT prevent release of dangerous criminals, or protect fellow prisoners from predation in prison. so the Church says that on capital puinishment there is room to argue both ways, and these are the factors of which one may argue. Capital punishment is not an intrinsic evil, but merely evil in certain circumstances.
ones from umbilical cords
There are stem cells and embryonic stem cells as a subset. All stem cells are useful in research. An example of non-embryonic stem cell is some umbilical cord cells. The Church opposes destruction of human life for research, and so it opposes embryonic stem cell research if it destroys the embryo. The Church does not oppose destructive research on non-embryonic stem cells or (if it can be done, which at this point is but s theoretical possibility) research on human embryos that does not endanger them.
It's also clear that innocent people can still be harmed or killed by some who are in prison. Drug kingpins and other crime bosses can still order murders from their cells. The murders they order can lead to the deaths of innocent people caught in the crossfire, so they are still a danger to society, as long as they're alive.
thanks for your excellent answer.
2267 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.”68
-CCC
The Church allows but discourages it. I’ve heard good arguments pro and con.