So is that why the rich are taxed at higher rate..
No, that's because they are affected less by the same percentage of taxation.
As this obviously isn't obvious to everyone, I'll explain:
Say the minimum cost of living for a certain time is 100, and citizen A earns 150, then person a has 20 left.
If we then introduce citizen B, who earns 200, then that person has 100 percent left.
If we tax them equally, say 20%, citizen A pays 30 and citizen B pays 40.
As this might sound fair, it really isn't. Why?
Because citizen A:s "discretionary income", as it is called, has shrunk by 60% and citizen B:s with only 40%.
So citizen A:s life will be far more more affected by the "fair" taxation than citizen B:s.
Also, the citizen with the higher salary will significantly benefit from the system, as that person will be able to invest his income, an yield a return, far easier than the one with the lower income.
As a consequense, most people over a certain income will almost certainly become richer, and most people under a certain income will almost certainly become poorer.
Widening income gaps has a number of other detrimental effects on countries, the most obvious, of course, is discontent but also a lessened interest in education. Why educate yourself when it won't make you make enough money to pass that barrier? Whatever, your parents can't afford college for you anyway, they have enough just sustaining the family.
This is an issue everywhere but especially in the "developed" world, where it simply isn't sufficient to have only a well-educated elite. Almost the entire population has to be well-educated to be able to compete internationally as a country.
The only solution is a progressive taxation system. And setting the level of progressivity is a simple math problem, easy to adjust to the effects of other taxes and to the taste of the current administration.
This especially kills off a host of counter arguments, since they were concieved before these things could be easily calculated(before spreadsheets, computers).
Personally, I pay the highest level of taxes in my country, and I don't wine about it.
There are upsides to paying taxes, too. In a working society, you get stuff back now and then.
Especially when you really need it. For example, if I get sick. Or if I need to hire educated people.