Progressive Taxation (Pro) vs Flat Taxation (Con)

Round 1.) Progressive Taxation is More Fair Than Flat TaxationConsider the following thought experiment: We have two people in our scenario, one earning $1,000,000/year in income, who we will call Joe, the other earning $10,000/year, named Peter. Let's examine the effects of each tax plan to determine the effects of each plan on both of our citizens.Example 1: Flat TaxLet's take a 10% flat tax, a commonly proposed plan, for exampleJoe pays $100,000 in federal income taxes, 10% of his income*. This means that he has $900,000 left, excluding state and local taxes.Peter pays $1,000 federal income taxes, 10% of his income. This means that he has $9,000 left, excluding state and local taxes.Now, what does this mean?Well, we know that the poor have lower amounts of disposable income and spend a higher amount of their income on basic needs, such as food, shelter/rent, medical expenses, etc.[2]http://s.wsj.net...[3]http://cdn.theatlantic.com...These are vital. The question then becomes, which means (because money has value) more: $1,000 to a poor person or $100,000 to a rich person? For Joe, that $100,000 is the difference between a vacation to Hawaii and a summer at home. Woe is he. As for Peter, that money is the difference between putting a meal on the table or not, paying the rent or going homeless, paying the energy bill, or going cold, etc. If a medical emergency happens to Peter, on the contrary, how is he supposed to pay for treatment? How is Peter to save for retirement? How is Peter to pay for his childrens' college? How is he to put food on the table? Peter needs that money to provide for his needs, whereas Joe wants it to provide for his desires. Many people do perfectly fine with $900,000 and still live lives of luxury. If needs matter more than wants, than $1,000 to a poor person means more than $100,000 to a rich person. As such, a flat tax system is unfair.Example 2: Progressive TaxUnder this example, Joe is taxed at 15% of his income and Peter at 5%**Joe pays $150,000 in federal income taxes, 15% of his income. This means that he has $850,000 left, excluding state and local taxes.Peter pays $500 federal income taxes, 5% of his income. This means that he has $9,500 left, excluding state and local taxes.Let's revisit the effects of our tax plan on the people, because that's what really matters when crafting our plan.Under this new progressive tax, Peter has more money, so he might be able to have a slightly easier time paying for food, affording rent, providing for his children, etc. His needs are better met under a progressive tax than under a flat tax. ***As for Joe, he is slightly worse off, but in the grand scheme of things, $850,000 dollars can still afford a life of luxury, all of Joe's needs are met, and many of his wants are too. His needs are met.If under a flat tax, only the needs of Joe are met, and in a progressive tax, both Peter and Joe have their needs met, the progressive tax system is obviously more equitable and fair than a flat tax system.*Joe would likely pay less as he can exploit capital gains loopholes, deductions, etc. even in a flat tax system, which ironically might end up being regressive:[1]https://www.washingtonpost.com...;**This is just a hypothetical, and seems the most plausible as a high tax rate would likely be in effect detrimental to poorer citizens, for the reasons desrcibed in the argument***Once again, a hypothetical, but it is true that the poor are generally better off under plans which are progressive, as they are taxed less.