> Inequality is based on random luck of birth.

We are each unequal to each other, yes. So what? Why is that bad? Why is equality good?

> It seems that you’re defending capitalism.

I'm not defending or attacking capitalism. I'm attacking the thoughtlessly repeated presupposition that inequality is bad as such. There is no justification for the claim that we should all be equally rich.

Because we should all have the opportunity to live good respectable lives. That's way easier if you chose better parents before you were born, but for those that chose their parents poorly, they shouldn't be penalized and should still have every opportunity.