The difference is that the rich person doesn't have to work. Their income is just the return on their investments. Meanwhile the poor person has to work 16 hour days to achieve an equivalent lifestyle. Okay, so they're paying the same amount of taxes, but is this a just way to organize society? What opportunity does the wage slave have to decrease their workload?

It's fine to have haves and have-nots, but the burden of supporting society should be equally borne, financially by those with financial means and laboriously by those putting in the labor. Regressive taxes force those without capital to pay twice.