Sure, we could tax all sales at 20%, or 45%. That would be fair. Can you see any problems?
We could tax everyone a flat amount - $10k or something. That would be fair. Can you see any problems?
We could tax everyone a flat percentage - 15%, say. That would be fair. Can you see any problems?
We could tax everyone such that we all have the same income - $50k perhaps. That would be fair. Can you see any problems?
The idea that higher taxes "punish" the rich doesn't make sense to me. We have the money! Of course that's where taxes should come from. What, we're going to shake down the people making $12 /hour? They don't have any money.
Here is my thinking: we should decide, as a society, what is essential. Defense, roads, fire departments, schools, etc. And then we figure out the best tax system to pay for that. We should aim for that system to:
1) Gather as much money as we need to pay for the essentials.
2) Cost as little to administer as possible.
3) Discourage harmful societal behaviour and/or encourage beneficial societal behaviour (generally, the more you tax something, the less of that thing you get).
4) Impact people's lives as little as possible. This is where progressive taxation wins - if you tax a poor person, that's money they really, really need. They were going to spend that on essentials. If you tax a rich person, their quality of life isn't meaningfully impacted. If Jeff Bezos has to pay more taxes, that impacts his day-to-day life exactly not at all.
5) Be conceived from behind the 'veil of ignorance', as much as possible. (This is where the 'fairness' argument comes in)