People seem to misunderstand my stance with equality. I do not believe equal treatment is necessary regardless of ability or performance. I believe that the opportunity to be successful or rich, a failure or poor, or just an average person, should be equal for everyone.
As a way to express it, in my perfect world the people born into the bottom 20% of the social and economic ladder should have the same odds of being in the top 20% of the social and economic ladder by the end of their life as somebody born in the top 20%. Regardless of your starting point in life, I believe you should be able to compete on a level playing field for rewards in life. A child born to rich parents should not have an inherent advantage over a child born to poor parents. Your own ability and merits should decide your future, not your birth.
Therefore, when I see two people who are equally qualified and working identical jobs, yet the pay is not identical, I see inequality. When a child is born into a poor family, and must therefore attend a school of lower quality than the child who's parents can afford a better private school, that is inequality.
And unfortunately, these are the circumstances of reality. Rich people will ultimately stay rich. If I remember correctly, around 60% of all people who are born into the top 20% of society stay at the top, with the majority of the remainder staying in the top 40%. Meanwhile, somewhere around 80% of all people born at the bottom stay at the bottom, with almost nobody making it into the top 40%. Not only are people who are born rich more likely to stay rich, but people who are born poor are more likely to stay poor, and experience less overall social and economic mobility (basically you move slower up the economic ladder the lower you are on the ladder).