In theory, organ donation is a very good thing. Even Pope John Paul 2 has endorsed the concept.
In practice, once you’re not just merely dead, but really, really, truly dead, many of your organs are unusable for donation. Therefore some hospitals will take organs from a person who is “kinda-dead” e.g. brain-dead but their heart is still beating. Or the heart stops beating, and rather than performing simple procedures to give it a jump-start, the person is declared dead and the organs are removed.
That is the crux of the debate, defining the circumstances under which you want your organs to be donated, to ensure that the organ donation does not become a murder.
catholiceducation.org/articles/medical_ethics/me0019.html
wf-f.org/NHBDupdate-valko.html