I believe the main reason for inequality in human society is that we live in a system full of institutions, history, and disparities in resource distribution. Take the gap between the rich and the poor, for example—things like education, healthcare, and opportunities are not equally accessible to everyone. Those who already have more resources tend to acquire even more, while those in poverty often struggle to change their situation.
If we compare this to animal societies, many animals also experience inequality. For example, in a wolf pack, only the strongest wolf becomes the "alpha" and gets to eat first and choose its mate. This inequality is direct and based on strength. But these hierarchies are typically for survival, and are natural and unchanging.
In human society, however, the layers of inequality are much more complex. It’s not just about wealth and physical strength, but also race, gender, education, and other factors. What’s worse is that in human society, there are many systemic inequalities—like the wealth gap and unequal opportunities—that are created by humans themselves. Many times, even when we know these inequalities exist, we lack the motivation or power to break them.
I cannot really pinpoint why there is disparities among humans but this has been a long lasting issue with humans, dating from when we had the monarchy system, where the king and his immediate family get special treatment, including members of the Royal dinasty. So historically we've heard classism. The modern era has its own form of classism, which to a large extent have been questioned by human right activist and people who have pushed for social equity, this has lead to people asking for a more democratic way of leadership so that the gap between the HAVE and the HAVE NOT can be bridged easily. So in a bid to fight this inequality in our society, we need strong institutions, this strong institutions can only be birthed with transparency in leadership, but once we begin to have leadership failure, then we will all be experiencing a lopsided system that breeds societal inequalities.