It seems to me that most average people opposed to higher taxes on higher income brackets (aka progressive taxation) don't actually understand the tax system at all.
There are two common arguments used against progressive taxation (and to some extent against income taxes in general).
The first is charity. It relies on the idea that government should not be providing social welfare, that all social welfare programs should come from individual charity, and that if government did not tax the populace at a higher rate to provide these welfare services that the populace would have more money to give to charity.
The second is similar. It relies on the idea that rich business owners (the highest tax bracket) provide jobs to all people on lower tax brackets, and that if government did not tax rich business owners at a higher rate then the rich business owners would have more money to expand their businesses, leading to more jobs for everyone else.
Both of these premises are contingent upon a similar misunderstanding of our tax system: we are not taxed purely on revenue. We are taxed on revenue minus deductions.
Giving to charity is a deduction. Taxes are collected specifically on income that is not being used to give to charity. If the people in question wanted to give more to charity, they could do so and their actual taxes owed would be lower as a result. The amount given to charity would not be counted as part of their taxable income. Reducing the tax rate would not give you one more dime to spend on charity, because the tax rate only applies to income that is not being used for charity in the first place.
Similarly, business expenses are deductions. Businesses are not taxed purely on revenue, but on revenue minus expenses. Another word for revenue minus expenses is profit. So businesses are taxed on profit. If a business wanted to expand and hire more people, the wages for these new workers (and new equipment, and new materials, etc) would be a deductible expense. And, in fact, expanding the business would reduce the taxes owed by the business owner because the money spent on those expansions would not be counted as part of their taxable income. Reducing the tax rate on profits would not give business owners one more dime to spend on expanding their business, because the tax rate only applies to income that is not being used to expand the business in the first place.
These arguments were originally made by people who do understand the tax code, who do understand that all higher tax rates mean is that they can't pocket as much profit for themselves. Who also understand that reductions in the tax rate for the highest tax brackets has lead to less money being invested in business, while the pay rate for CEOs and owners has soared to 400 times that of the average worker, compared to a mere 20 times as it was for much of the past century and as it remains in other parts of the world such as Canada and England. But they are arguments that have been swallowed by many who do not understand the tax code themselves. Let's work on explaining it to them.