Taxing everyone that same percentage may seem fair, but without other taxes in place what that does is hamper lower earners' ability to afford basic living costs, or deprives tax income from higher earners that can afford it.
Ultimately it comes down to the fact that not everyone in the country earns a good wage, and society is reliant on people that do earn to prop up the lower end.
This may not seem fair, but those people at the lower end may not just be there due to laziness or other perceived negative traits. Maybe they went to a bad school, had to care for a parent or relative, or a myriad of other reasons for not achieving as highly as others. At the other end, higher earners may have had a boost in life from coming from a wealthy family (private tuition, a network of contacts setup by their family in the business world, etc) that makes their position seem unfair.
I could argue it is not moral to keep money that is purely disposable income that could be used better elsewhere, through tax, to benefit the less fortunate. The truth is probably a balance between the two, hence the current model of tax brackets.