10% of $15,000 is $1,500.

$150 is 1%, no offence but maybe you shouldn’t be in charge of the math.

Because basic living costs money. Also your math is bad. Your examples reflect a 1% tax rate, not 10%. I'm assuming you picked $15k as a number because that's full time at federal minimum wage. Imagine paying for a month of rent, utilities, groceries, car payment, gas, insurance, and anything else that's necessary with only $1250, and then you still owe $1500 in taxes for the year. Hopefully that's the combined state and federal taxes and not just federal, but there's still sales tax to worry about.

On the other hand, 10% of a billion dollars is $100,000,000. Taking that amount from a billionaire leaves them with only $900,000,000. How on Earth can they be expected to make ends meet?! /s. The reality is that survival has a high floor, but many Americans live in the metaphorical basement (and in many cases a literal basement). There's virtually no difference between having $1B and $900M, but there's a massive difference between having $15k and $13.5k, and that difference means having sleep for dinner every other night. Show me a billionaire who has to choose between eating and having electricity, and then we'll talk about flat tax rates.

It's just shitty for poor people, because they spend a much greater percentage of their income on basic necessities. So a flat tax hits them extra hard. A simple progressive tax is so much better for the working class and not that much more complicated.

If it helps, don't think of our current system as a progressive tax, but think of it as a flat tax with discounts for being poor. The less you make, the higher the discount. Because 10% is not nearly enough money to pay for everything we need.

Rent, food, transportation, utilities, education, these are fixed costs that don't scale linearly with income. You might spend more on fresh vegetables or rent a nicer place if you have the money, but generally speaking the first $50k of anyone's income is going towards just existing. If you make less than that in the United States, you need every penny, and you probably need government services to help you survive. A flat 10% tax would probably kill you.

It's in (almost) everyone's best interest that nobody is struggling to survive. Social services help everyone at rates exponential to what they cost.

If you make $100k, congratulations, you can probably afford a starter house in some parts of the country. You might be able to save up for a vacation. You can begin to think about having kids (oh shit, did you already have kids? Because they're expensive as shit). You can afford a 10% tax with good budgeting.

If you make $500k per year, congratulations, you're wealthy. You can afford the American Dream of a house, a family, a dog, a yard, a car, and a retirement account all at the same time. You can also afford to pay far more than 10% without impacting your ability to pay for all those things.

The more you make, the smaller percentage of money you need. The higher you go, the worse it is for everyone if you simply keep all of your income. If you're making $10 million every year, you could pay 80% taxes and still have four times as much as the wealthy person described above.

High concentrations of wealth are bad for society. Coincidentally, the uber wealthy are the only ones that benefit from the suffering of poor people. As consumers and/or employees, people are easier to exploit when they are desperate, and everyone who amasses wealth is exploiting someone.