Rationale for a flat tax?

My reasoning for opposing a flat tax would always come down to a scenario: let's say that income tax rates were at 20% annually. You have 2 families: one who makes 300,000 a year (upper middle class/rich), while the other makes 50,000 a year (working class, and note that this is the average American salary). If you take away 60,000 a year, giving them only 240,000 for themselves, that could just mean that it would be another year before they can afford to send their kid to Georgetown or Harvard. However, if you take away 10,000 a year giving a family only 40,000 a year, that is much more detrimental to the livelihood of the family. Am I making a valid argument that a flat tax tends to favor the rich over most Americans? What's the justification for the Republican party favoring a flat tax?