Yale psychology professor Paul Bloom's 2016 book, Against Empathy: The Case for Rational Compassion deals with what I think you're trying to say Zolotiyeruki. The argument seems counter intuitive to most people, but if you think about it, it makes a lot of sense. Sometimes, empathy for individual cases leads to arguably immoral/unethical outcomes.
I'm glad you had the "sometimes". I made the example above as to how the hoped for repeal of the ACA by Republicans would cause a man's wife to die because she couldn't receive health treatment to help her live.
I think most of us would have empathy for this individual case. Why would we have this empathy? It is because we know that what happened to the man's wife could happen to ourselves or our loved ones.
How would this be immoral? Perhaps the money spent on the ACA would have been spent on an even more moral expenditure. I cannot imagine what could be more moral than saving innocent people's lives. Perhaps the man's wife was a serial killer and would have taken more lives that her own. It could have then been judged immoral to save her.
It struck me at the time and still does that the hoped for repeal of the ACA was immoral. I cannot imagine how the repeal could have been more moral than the retention. Most of us value human lives. This is at the core of our beliefs. Retaining the ACA saved lives. The jettison of the ACA would have caused the loss of lives.
I do not think the empathy for the man's wife and the many other lives saved by the retention of this law was one of those "sometime" examples which led to an unethical / immoral outcome. Disease can strike any of us at any time. This law did not pick winners and losers among the population it helped. The intent of the law was of a high moral purpose in saving lives and improving the quality of said lives.
You may make the counter-argument that winners and losers were picked since the healthy are to subsidize the unhealthy. This is weak. Even the strongest most fit individuals have succumbed to disease. You may say that this is a small percentage of the healthy population that succumbs to disease. This leads us back to the individual and empathy. For that individual could be you.
Stalin said, "One death is a tragedy. A million lives is a statistic." Don't think like Stalin. All human deaths are tragedies. The ACA has been a good start in avoiding Stalin's statistic.