My specific diagnosis which tends to be confirmed the more I read, is that what is not equal is that more and more surplus is vacuumed towards the top. Every year fewer and fewer people own more and more of the wealth; Oxfam does about the most prominent report about this, and it's disquieting to look at a few of those reports in succession--every year they report some bizarrely small number of people whose wealth is equal to the wealth of the bottom half of people in the world, and then next year that number is even bizarrely smaller.
This is a very strong tendency in our economic system. It can be interrupted and temporarily reversed by major social upheavals, such as the massive unrest of the Great Depression, but in times of relative status quo the wealthiest use their power to gradually re-rig things to favour them more and more, so that the gains from such things as technological improvements are not distributed across the whole population but go almost entirely to the wealthiest--mainly such people as large shareholders and other owners of firms, but also big landowners and so on.

Now, it's easy to look at the specific billionaires involved and conclude that this has something to do with people being greedy, venal and crooked, but that would be a mistake. It goes back to the basic nature, in fact the basic strengths, of capitalism. The point of capitalism is for private individuals to invest in things which make a profit, so that they end up with more capital to invest, to produce more, to make bigger profits and so on. Capitalists are supposed to maximize returns; this is how economic activity is grown. The hope is that all this maximizing of returns to investment involves something productive and useful being done, so the results will be positive. Unfortunately, there are problems; I'll mention two really big ones.

First, a sort of collective action problem for capitalists, where each maximizes returns by minimizing pay to the workforce, but each depends on the buying power of all the other capitalists' workforce. So each capitalist may be busily increasing production by paring down what they spend on labour (among other costs) and reinvesting the profits, and the increased production from that individual firm may be growing the economy, and that might seem to compensate for those workers getting less money. The problem is, it's the workers that are expected to buy the products, and if all the other firm owners are doing the same thing, collective demand will stagnate and choke off economic growth overall. That's one reason overall growth since the Reagan/Thatcher shift has averaged lower. But individual capitalists can't just say, well, I'll pay my workers better and take a short term hit to profits so people will be able to buy products, because a competitor who does not do that will make higher profits or be able to undersell him. Any firm that learns the meaning of the word "enough" will be out-competed by firms which do not. So as demand stagnates, firms will just keep doubling down on minimizing labour costs, squeezing the workforce further.
(For some time now, we've been creating demand without higher wages by increasing debt, but that has limits and causes a host of problems)

The second is that the whole idea of beneficial capitalism assumes a sort of given playing field, but in reality one of the major concerns of the wealthy is to rig the playing field. Modern economics normally assumes that politics and economics are separate, but in an era where legislation is often written by corporate lobbyists and passed by legislatures without a comma of alteration, that is clearly not the case. If you have a structure in which the goal, and the way to gain power, is maximization of profits, and so the people with the wealth and power got there by an ethos of profit maximization by any means, inevitably many of them will figure out that getting those profits by effortful processes of developing, producing and marketing products is kind of doing it the hard way. Investing in the creation of tax loopholes, legalizing externalities (basically saving money by unloading "bads" on the general public, whether by lax safety, environmental destruction or whatever), the enabling of financial maneuvers that under different rulesets might be considered fraud, or such giveaways as Quantitative Easing . . . the money spent buying policies where the state one way or another effectively gives public goods to the private wealthy often has far higher returns than normal productive capitalist endeavours. But it comes from the same basic set of goals and motivations; in both cases you're investing money (in campaign finance, PR firms, lobbyists etc) to gain a return on investment. So it's not froth on top of the system, it is built deeply into it. You can see this same sort of thing in operation from before Adam Smith's time; the very availability of a workforce for factory employment in the early industrial revolution was created by such things as the Enclosures, legal maneuvers taking land away from small farmers so that they were left with no means of support, combined with a massive increase in draconian heavily-enforced anti-vagrancy, anti-poaching and so forth laws. The class of people who ended up working in factories was created by legal interventions heavily lobbied for by the wealthy people who needed an expanded workforce. Now one could argue that whether created by a rigging of the playing field or not, the results of the industrial revolution were a dynamic unleashing of production so it's OK. Leaving aside some of the problems back then, the problem nowadays is that they can't say "enough"--as I've said, it's structurally impossible. So as with normal production and the tendency to never stop trying to squeeze wages and other expenses, those rigging the legal structure can never say "Good enough, we've got big advantages over the proles let's leave it at that"; if some of them do, others will come along who don't. Thus for as long as there are no major upheavals, the very structure of society will continue to get shifted by those with the power to shift it.

Between those two problems (and a number of others), at any given time, one might be able to say "Well, this is more or less OK (for me at least); and if things stay like this and technology keeps improving boats will get lifted"--but things can't stay like this, the tweaks, the progressive unbalancing, will continue because those doing the tweaking have no stopping point. So things will keep getting more unequal until either the majority put their foot down or there is a major economic crisis. Even then, if we just recalibrate a la New Deal, leaving the wealth and power at the top diminished but fundamentally in the same structural position, they will just start up where they left off, bringing us to another peak of inequality and instability a few decades down the road. Unless civilization falls due to global warming.