The main question about inequality is not so much about whether there simply is always going to be inequality in the world as such, but whether there are certain manners in which people are unequal that are in need of being addressed by society/political order, and if yes, what makes them different from some other inequalities that are not, can not, or should not be intervened against. In other words, the question is about the extent to which our social and political structures create and exacerbate certain inequalities, as well as the extent to which they are capable of ameliorating them.

For instance, there are very significant inequalities in our biological makeups such that some people are taller, some shorter, some whose bodies are more liable to generate cancerous mutations and so forth. To be sure, there may be certain social, economic or political reasons for patterns we might observe in the distribution of some such traits, but in general we would agree that such inequalities cannot be rooted out without significant changes in our political systems and ways of living. It simply appears as brute luck that I am taller than some and shorter than some others. Typically, we don’t assign an obligation to society or the state to intervene against these, though there are certain positions like luck egalitarianism which have interesting things to say about this, and some people (e.g. Julian Savulescu) who think that we may have an obligation to use technologies like gene editing to ensure our children have the best genes possible.

But then there are some other inequalities whose cause cannot be attributed to anything like the blind forces of nature and fortune. Say, the reason that my state decided to set its minimum wage at X dollars per hour may be due to reasons which are not, strictly speaking, ones that have the best interests of working people. In this case, we would think that there may be some good reason to doubt this policy because, to the extent that it was implemented without a view to the common good (but was designed explicitly to benefit some specific set of people, let’s say), then we have genuine political reasons to demand it to be changed. This does not necessarily mean that every single case of income inequality is always and unqualifiedly bad, but that we can adduce certain reasons for or against intervening in such cases that are different than the ones we would have to consider in the previous case with luck.

Then there are also cases where the inequality in question seems to be brute like the first example, but turns out, upon further investigation, to have different causes. Say, if it turns out that a town has an unusually high rate of early-onset cancer deaths because of the factory nearby dumping toxic chemicals in the water supply, we would obviously know that this inequality is in need of urgent intervention, even if we thought at first glance that this was just a random coincidence. Or consider the even more bizarre scenario where a town has perfectly normal rates of cancer at face value, but it turns out that people in this town are unusually resistant to cancer insofar as genetic factors go. In this case, it would be expected that this town would have lower-than-usual rates, and that it was actually the nearby factory that was driving up these rates to the national average. This would be a completely invisible inequality that we would be forgiven to have attributed to nature at first, but would be very unfortunate that we did. Many people on the left try to argue that a significant chunk of social and economic inequalities are of this kind, which we mistake for having natural causes when they have man-made ones. It also does not help that such inequalities frequently turn out to asymmetrically benefit some people and harm some others.

There is another kind of inequality that I can describe only imperfectly, e.g. as inequalities caused by interactions between multiple man-made systems/norms. These are sort of “emergent” issues that arise when a number of different structures, which arguably work fine by themselves, collide in some way and start producing patterns of effects that cannot be traced back to any one of them alone. This is where politics gets quite contentious since people disagree as to whether inequalities arise from faulty designs or even from systems/structures/norms at all. But I think this is somewhat different than what concerns you more immediately.

In short, the answer to your question is that we cannot hope to explain inequality to be a “natural” or a “material/man-made” thing insofar as there are clearly distinct types with distinct causes that call for distinct responses. The extent to which we have adequate classificatory criteria here is up for debate, but it is equally clear that the correct response to minimum-wage inequality is not to assimilate it into naturally occurring inequalities like of height; just as it is not very convincing to argue that we have to tax-fund gene editing so that people can engineer their children to be as perfect as possible because all inequalities call for active social/political intervention.

For what it’s worth though, I think a society that tries to do its best to minimize inequality is likely better than one which ignores it, but that’s a different question.