Student or Learner
Does this mean saving a girl in great pain can be immoral when two old ladies are almost dying? If you are attracted to a beautiful girl, you may do so. I can't think of a good example to differentiate compassion and morality.
We can see the occasional clash between compassion and morality in the lab. ① Experiments by the psychologist C. Daniel Batson and his colleagues find that being asked to adopt someone else’s perspective makes participants more likely to favor that person over others. ② For example, they are more prone to move a suffering girl ahead of everyone else on a waiting list for a lifesaving procedure. ③ This is compassionate, but it’s not moral, since this sort of decision should be based on objective and fair procedures, not on who causes the most intense emotional reaction. ⑤ Part of being a good person, then, involves one’s compassion, not cultivating it.
Yes, it's saying that a compassionate act can be immoral.
If three people turn up for treatment, and the last person who turns up is a beautiful young girl who you feel compassion for, then choosing her to treat first is immoral. Morality compels you to treat the first person first (given equal seriousness of the problem).
If a judge lets his murdering daughter off punishment, that's immoral, but based on compassion. (Not that a judge would be given that task).
I don't know what the last sentence is supposed to mean though. It's not proper English, unless it means "not cultivating compassion", in which case, I'd disagree.