There is nothing inherently fallacious about appealing to emotion unless one misunderstands the appeal to emotion fallacy.
In the first place, emotion and rationality are inseparable*. One needs to emotionally care, as an assumed axiom, in order to govern rational decisions — moral decisions in particular. The common notion that there is a dichotomy between emotion and rationality is false.
The appeal to emotion fallacy is along the lines of a non sequitur — a disassociation with the argument at hand; or even a false dilemma, but because the emotional impact may be powerful it obscures the mismatch.
The linked example is helpful,
Example: Luke didn't want to eat his sheep's brains with chopped liver and brussel sprouts, but his father told him to think about the poor, starving children in a third world country who weren't fortunate enough to have any food at all.
The starving children in third world countries is an unfortunate and vivid image, but has very little to do with the practical reasons of what Luke is being served.** There will always be starving children somewhere, but this doesn’t demand that Luke has to eat what he doesn’t like. This is what makes his fathers argument a fallacy. Because Luke may be made to feel privileged and guilty he may yield on pressing the discussion further.
Making an argument that we shouldn’t harm others because we wouldn’t like it if someone harmed us, which is essentially the argument you are critiquing, is very much an appeal to emotion. However, it isn’t irrelevant! This concept is the basis for most of the better moral frameworks, secular or religious.
Fundamentally, all moral arguments are an appeal to our emotional sentience; it’s what makes us care about anything in the first place and recognizing it in others is what makes us care about them.
Rationality is driven by emotion. Most people aren’t persuaded by cold facts. To be persuasive, one needs to pluck at the heartstrings of an audience. Images are effective. Personal narrative is useful. An emotive and empathic presentation style goes a long way; it’s easier to be persuaded by someone who is friendly and relatable.
Accurate facts are still required, but reaching people on an emotional level or including emotional pleas in an argument isn’t an automatic fallacy so long as the sympathetic associations are inseparable from the topic and isn’t mere rhetorical subterfuge.
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* Reference David Hume in classical philosophy, “reason is a slave to the passions.” Also note neurological data where people whose emotional areas of their brains are damaged become “hyper-rational,” but have great difficulty making decisions because they can’t fundamentally care on an emotional level. The first half of this blog post,
How Emotion Shapes Decision Making, explains the phenomenon, and I highly recommend the first part of this RadioLab episode,
Overcome By Emotion (00:00 - 06:30).
** The example isn’t perfect. If Luke’s family isn’t well off, and the food his father is serving him is all that they could get, then referencing starvation and gratitude at having anything to eat at all isn’t a baseless argument. But I don’t think we’re meant to read too much into the example. Basically, there may be good reasons for Luke to eat food he doesn’t like, but those reasons should probably be local and specific to him before leaping for reasons in another continent.