Many voters in the middle class feel like they've worked (and continue to work) very hard to get where they are and object to the meager spoils of their work being taken for redistribution. Right or wrong, it's a very real feeling. (Obviously, I'm not saying dollars are kidneys, but they will cause a similar reaction in people.)
I think that type of reasoning is fallacious because every policy leaves a subset of people worse off (you can just choose your preferred subset to make the point). Including the status quo.
I like your kidney analogy, and I think it makes a strong counter point that is worth considering when weighing up policy ideas.
Though, the status quo in that analogy looks to me like the majority of people in the world currently are having one kidney removed during childhood, mostly to feed the middle classes and build toys for them. Some unlucky ones have two; they are sick and dying. But we couldn't take a kidney from the healthy middle class folks to give back to those, could we, because voters in the middle class feel like they've worked (and continue to work) very hard to get their kidney from some unspecified source we don't like to think about, and they object to the meager spoils of their hard-earned spare kidney being taken for redistribution back to the people they came from.
Refuting dumb ideas to help the poor doesn’t mean I don’t care about helping them.
Any cash given to the poorer classes and taken from the middle classes likely has greater quality of life value to the poorer classes - because it would be used for things that are more essential to life.
This means the quality of life loss to the middle classes is more than offset by quality of life gain to the poorer classes. And the poorer classes have many more people.
By some ethical standards, this makes it unequivocally beneficial to redistribute.
(I don't actually agree with that approach, because money in some hands is more potent for creating benefit to others, than in other hands. But I think the parent's argument, that it's bad because the middle class would suffer, is essentially a "poor people don't matter" argument.)