Why flat tax rate is unfair

If the nation were to implement a flat tax rate, it would only make the wealthy wealthier. This reason for this is, say the national tax rate is 10% and you have two people, one who makes 25,000 a year and one who makes 1,000,000 a year. After taxes, the person making a million dollars would still have 900,000 but the person who makes 25,000 now only has 22,500 and it is much more damaging to their ability to survive off their income.

Now, in a progressive tax system, if a working-class person were to 0% taxes on their 25,000$ income. However, the person making 1,000,000 now has a 50% tax rate. The person making 25,000$ a year may still be able to survive and the person making 1,000,000 can still live comfortably on 500,000$ a year.