A very common myth, even one perpetuated by economists, is that utility means happiness, pleasure, satisfaction, the avoidance of pain, or something like those things. That is not what utility means.
To understand and predict behavior, we need to know what people value. For example, will Alice choose green beans or asparagus? That depends on which one she values more. Why did Bob willingly tire himself and expend energy at the gym? Because he values being fit. Instantly we run into two problems:
1. We don't know what people's values are.
2. People value different things.
Most people's values clearly include things like happiness, pleasure, satisfaction, and the avoidance of pain. But there are people who eschew earthly pleasure. There are people who's self-destructive behavior seems almost deliberately aimed at preventing their own happiness. People willingly bear pain for many purposes and even seek pain and painful experiences out, whether something drastic and worrying like cutting themselves, or something more mundane to a degree like punishing themselves at the gym, or even emotional pain like calling up that ex-lover. (See What Do People Want to Feel and Why?) Are all these people and their actions outside the scope of economics?
It is also a mistake to think that all values have to be sensations. Sometimes people make the mistake of thinking that death must carry infinite negative utility. That would be true if the only values were bodily sensations. However, people can also value things external to themselves, like the lives of their children or comrades, even at the expense of being able to feel bodily sensations about them. People suffer and sacrifice to write a novel, to start a business, to build a house, to create democracy, to help the impoverished and the victims of earthquakes, famines, and wars. Are all these people and their actions outside the scope of economics?
People are not happiness maximizers, pain minimizers, pleasure optimizers, or any other such thing, although particular individuals might be. We need a word that simultaneously expresses our ignorance in a concise manner and unites the many diverse values under the economizing paradigm. That word is utility. That way people don't say, "But what are people maximizing?" because a scientific-sounding answer exists, and they don't say, "Economics might work for those values, but it doesn't work for my values," because utility is a placeholder for any value. And that is very important and necessary, but it has clearly caused some confusion among economists.
Interpersonal utility comparisons are impossible not because of some property of utility, because utility has no properties. Utility is not even nothing. It is not a thing. It is a mere placeholder, simultaneously expressing our ignorance of people's values and the proposition that the pursuit of values in general has certain general properties, regardless of the particular value. Interpersonal utility comparisons are impossible because you can't compare [placeholder for ignorance and the idea that all values fit into the economizing paradigm] between people. Rather, you must know that people have the same values, which you very rarely do.
Here's a question for economists who think utility means happiness or some other particular value: if scientists discovered a planet full of sadness maximizers, would you think that the utility maximization paradigm does not apply to them?