Why do you want the rich to pay more, simply because they can? Isn't that a bit arbitrary?
The rich get major advantages from the state and federal government simply due to the amount of money they have. For instance, take a rich and a poor family. Who gets to send their kids to a better school? Why should a poor person have to pay the same amount of tax in order to get a ****tier service?
Now apply that to other government services. Who has better policing? Cleaner streets? The list goes on and on.
The rich gets to send their kids to a better school by paying more for it. Better schools are fairly expensive, at least around my part of the U.S.
That's still leaving aside that while the tax rate may be the same, that is in no way besides that the same amount of tax. It's not like they're both paying a flat $5000 each or some strange sum like that. They would pay the same proportion of their income, which would necessarily be different in they earn different amounts.
Say there was a flat tax of, say, 20%. A person making $30,000 would pay $6,000, leaving $24,000, which is still 80% of his/her income. A person making $250,000 would pay $50,000, also leaving 80%, but paying in an absolute sense a whole hell of a lot more. $24,000 is still enough to live on, so it's not as if it isn't fair to anyone.