Of course none of that ties income tax brackets in with the chart that you showed. You can tax the rich, and create welfare programs, or even reduce taxes, on the lower end all you want... it will not change the reported income of those people.
You keep coming back to some notion of a pie where someone is getting a bigger slice than someone else. This is not how economics works. There is no spoon, and there is no pie. You don't get a slice of it, your ability to create value for yourself is not dependent on whether or not someone else does. The 1 person with 35% in your example does not cause the sizes of anyone else's wealth to be what they are. 40 people in that example had 1%. But those 40 people do not have to take anything from anyone else to double the amount of value they create... or magnify it by a factor of 100. It is entirely within their control. Why should I not "accept" that people have the wealth they create?
What's happening to you (and so many others) is that you're coming face-to-face with the nonlinearity of economics. Property creates wealth on its own. Because it is valuable, because it "works" on its own (if you employ it). So the more property you have, the more wealth you can create. Again this is not harming others. That fact though, that more property creates more wealth, is a runaway effect. The more you have, the more wealth you can create. But you only ever have the wealth you create, you never create and subsequently own what other people are creating. That's their wealth. Keep in mind I'm not referring to currency or money, I'm referring to value, real value, not faked. It is only good for the world that more real value is created. Something valuable, which did not previously exist, was generated. No harm done. In fact, that's what we want.
*taxable income, which is not the same thing as income.
A person earning 25k in income has access to the standard deduction, reducing their taxable income to 13k. The total tax liability for that person is $1370. If they had a dependent child, the liability would be $0. If they were married, the liability would be $100. If they put $5k into a 401k, were unmarried, and had no children, the liability would be $800. If they put no money in an IRA, were unmarried, had no children, but were over the age of 65, the liability would be $1178. All of the above assumes no deductible property taxes or state taxes.
A single person earning $50k in income pays $4,370 (no IRA, no kids, no age exemption).
A single person earning $98k in income pays $14,900. With 1 dependent child, $12,930. and Married, $6,499. With $250/paycheck health insurance premiums paid through their employer.. $5,719... with a $5000 per year retirement plan contribution... $5119. Or with an $18,500 per year retirement plan contribution... $3500.