I have a more direct, ethics-based argument that many may find simply offensive, but I think the logic is pretty strong if people are willing to set their emotions and sense of entitlement aside for a minute and fairly consider the logic in this thesis:
The rich are worth it, the poor are not.
Now that's not universally true, but by and large, I think that's the principle driver of economic inequality in the US. People get paid what they are worth. Of course in a capitalist system, it is true by definition that absent manipulation of market forces, the market determines what jobs and products are worth, but I think there is a real logic/ethics to it (which is why I'm a capitalist):
It is taken as a given by an arguer against income inequality that incomes for everyone should be increasing by a similar rate. But why? Why assume everyone is worth equally more? Are they doing the same amount more work? The same amount harder work? Have the qualifications increased by equal fractions? Aside from the secondary supply and demand driver, it is illogical to think that people should get more money for the same job just because other people are getting richer. The fundamental problem behind it is this: Jobs at the bottom are not getting more demanding, therefore they aren't worth more money than they used to be. Examples:
Does a janitor today do more work than a janitor 30 years ago? So why does he deserve to get paid more? (both rhetorical: he doesn't).
I highly respect police officers. It is a thankless, difficult and dangerous job, but has the job of a beat cop changed much in the past 30 years? In some cases, use of technology may increase the breadth of the skillset, but beyond that, I doubt much has changed. So there shouldn't be much of a difference in pay.
A carpenter today is vastly more productive than a carpenter 30 years ago, so he should get vastly paid more, right? Wrong: the carpenter outputs more work, but inputs less effort than was required 30 years ago. If anything, he should be paid less, not more. The people who should be rewarded for the output of the carpenter are the ones who invented, produced, and bought the power tools that enable the carpenter to be more productive. The rich people.
A machinist. Depends on the type, but the industry has been revolutionized over the past 30 years or so with computers controlling them. A machinist with modern skills? Should probably get paid a lot more than a machinist 30 years ago.
Random office drone. Like the carpenter, they output a lot more than 30 years ago, but they do it because technology has made their job easier. Wow, you can use MS word?! So can my 12-year old (caveat: I don't have kids). So they aren't worth any more than 30 years ago. An awful lot of middle class, college educated people have such jobs, but they require no special skills or growth. They don't deserve more money. Short anecdote: I worked as a temp doing that kind of job while in high school and college - one company even fired their resident stoner and tried to hire me full time. Hell. No.
Engineers (me). The job has gotten more demanding as the demands on the industry and demand for the services have increased. The easiest way to demonstrate this is via the gradually (but continually) increasing requirements for aquiring a PE license. In addition, the job changes - perhaps not the complexity, but there is always innovation and therefore always more to learn. This job is worth more to society than 30 years ago. Not vastly more, but more.
Bill Gates, Steve Jobs, Jeff Bezos, whatever Walton was in charge, and a thousand others like them: These are some of the super-rich that people hate. They are fabulously wealthy, but seeing as how they revolutionized most of what we do in our daily lives over the past 30 years, I think they've earned it.
Oil tycoons. The original and reincarnated "robber barons". Except that the Sherman Act prevents the type of monopolistic abuses that made the original robber barons robber barons. So why do we hate the oil tycoons today? Because they're rich. Because we pay them a lot of money for their product. That's it. Waa. It is unfair and illogical that we fantasize and nostalgize the 49ers, but hate the guys who actually found the gold. Wait, maybe that's it: few of the 49ers actually got rich, so there's nothing to be jealous about! Waa. It's childish. These guys are lottery winners. Yeah, some luck goes into that, but sometimes getting rich takes some luck. It doesn't make sense to hate someone because they are lucky.
Money managers. These are the guys I have a problem with. And it isn't really even about being super-rich: many of the "just rich" got that way via the same business model. They've found a way to get paid based on taking a percentage of the medium that is the raw material/product that flows through their industry. That medium happens to be money. That would be like me getting paid in therms of gas or kWh of electricity that the systems I design use. It doesn't make sense to me. A mutual fund gets "loaded" at a percentage of the money in it, but that's not their product. The product is the investment strategy. The amount of money in a fund has no bearing whatsoever on the difficulty of an investment manager's job. That's a business model I'd like to see changed, but it is hard for me to hate people who for the most part just joined a flawed industry and didn't create it (this is why physicists are joining the industry). That said, the same attitude of entitlement that brought up this issue also motivates some to think they deserve what they get paid. Short anecdote: my sister is a financial analyst and had to listen to the traders whine over their lower bonuses in '08 and '09. They felt they deserved bonuses even though their funds lost money. I disagree.
Lawers. See: Money managers - the same logic applies. If you look, though, you can probably find a lawyer willing to work by the hour instead of on contingency.
I think I've rambled a bit here, but I'd like to see someone address the basic point: why should people who haven't substantially increased the skills or effort of a job be paid much more than their predicessors? Better yet, besides a little bit just for loyalty, why should someone who does exactly the same job they did 30 years ago (a 50 year old carpenter, for example) get paid more than they did 30 years ago? Their productivity (input) probably peaked 20 years ago!