Speaking as an undecided, who theoretically supports breed-to-cull (with exemptions) but can't defend Copenhagen's position...
While informed argument and a certain amount of skepticism is to be always encouraged, I also think that there should be deference and respect to experts. The Danes running the zoo are scientists and experts at what they do. Public opinion should not be ignored, but it should also not form the basis for decision-making. We have experts for a reason: so that they can make informed decisions about related affairs. With that in mind, while I have some reservations of my own about the incident and whether they made the right choice, I support the zoo's position of holding their ground and defending their actions, instead of bowing to public pressure.
Expertise in one field doesn't make one an expert in everything. Aren't ethicists, rather than scientists, the experts on whether this decision should have been taken?
But this is done with literally billions of animals every year. If it is ok to breed cattle, grow them out for a year or two and then kill them as they reach maturity, why is it not ok to do so with eland or giraffes?
If we're getting into the argument from equivalence, how about humanely euthanising human children after a year or two? You'd be hard-pressed to argue that a baby is more self-aware than a chimp, say, and it would be great experience for first-time mothers.
I think there are two primary reasons why the above is considered unethical. The first would be that human life is inherently special, but this a) requires justification applicable to every member of our species but no member of another species (good luck with that...), and b) highlights the hypocrisy of zoos (including Copenhagen) anthropomorphising, then dismissing the public backlash against culling. The second is that killing a human baby would adversely affect others, notably the mother, but again this applies to the Copenhagen example - thousands were outraged and upset by Marius's death.
In both respects, Marius was not equivalent to your average cow or pig, and Copenhagen's actions were mired in hypocrisy.
It's hypocritical to tacitly accept it for some species whilst raising an outcry about others.
I disagree, and the example you provide suggests you do, too. You describe giraffes and cattle as "directly comparable", but what about giraffes and jellyfish? Or primates and poriferans? In both cases, I think the invertebrates, which have neither self-awareness nor emotions, are less intrinsically valuable than the mammals, which are (potentially) capable of both.
Where to draw those lines will always be an issue but, unlike previous posters, I think a taxon-based approach is appropriate. In fact, one of my main bugbears with the "animal rights" movement is that it follows Orwell's seventh commandment: all animals are equal. This contradicts one of the few hard-and-fast rules of ecology: species differ. So, where is the moral obligation to treat them all the same?
As a general point, particularly pertaining to the discussion over "Disneyfication", you can go too far the other way (Denmarkation?). Would anyone here support adding lions to Copenhagen's giraffe enclosure, for example? I think not, because most accept we have a duty of care to zoo animals which we don't have to their wild conspecifics. Certainly the industry itself is structured on that assumption.