"Fair, in this sense, means equal."

Fair means corresponding to your ability, not equal. This is the same reason why elementary school and collegiate athletes do not compete against each other at sporting events.

"Works for me." No, it really doesn't. Implementing a flat tax model based on what the lowest-income citizens' ability to pay would reduce individual income taxes to nearly zero. This would eliminate almost half our federal tax revenue, and of course we are already operating at a deficit of $400+ billion per year. 

Let me guess: you want to cut spending to match that reduced revenue level, right? The problem with that is that paying our current obligations - Social Security to those who have already paid into it and service on the national debt for revenues already spent - would consume nearly all of it. We would have almost nothing left for defense, health, veteran's services, transportation, or anything else. That wouldn't work for you at all, even if you think it would.