Progressive tax systems function on two fundamental concepts: reasonableness and fairness.
Progressive taxes are reasonable: the poorest have less money to tax, and so provide little revenue at high tax rates. The lowest 20% of Americans, for example, earn 3% of the income, and the second quintile earns hardly more than 8%. A flat tax reduces the capacity to consume basic needs and to self-sustain, which then reduces taxable income by reducing jobs, creating a need for costly welfare.
Progressive taxes are also fair: our income levels are by and large determined by how much income we make per hour we work. An overall-wealthier household has, for its working history, earned more income than an overall-less-wealthy household, and thus has gained a greater benefit from society for the total of all effort taken by that household’s earners. That includes all effort developing any skills and knowledge, which have been paid back through earnings to make the household wealthier.
It is clear that wealthier households still rely on the labor of low-wage workers to bag groceries, ship goods, and handle the menial needs of our economy. These earners benefit from and should rightly support those who struggle to make ends meet, yet also deserve to keep their success as they are not at fault for the limited nature of opportunity. A higher tax rate for the higher-income earner can indeed leave them wealthy while calling them to take up a larger and fair share of the burden of our society.