I see and completely accept your point, but you need to look at things from the other side. Having a flat rate means that there is less money for your government to spend on welfare, healthcare, education etc. This means cuts have to be made.
- Cuts to the education sector means public schools have less funding, meaning a child who's parents who can't afford a private education has to suffer. This has the worst affect on your economy (I shouldn't have to explain why).
- Cuts to welfare mean some peoples incomes are drastically reduced, meaning they then struggle with bills and rent. This then increases homelessness which is a big problem in some countries already.
- Cuts to the healthcare sector mean longer wait times in A&E due to less nurses and doctors and potential a increase to the price of prescriptions for medication, this now mean they struggle to pay for medication they need.
I know you'll probably say "why don't they just get a job?" a lot of people do, but still struggle to make ends meet. Also, with a flat tax you simply allow the rich to get richer and put nothing back into your country.