Income inequality doesn't bother me as much as inherited wealth.
Family Wealth Lasts For Ten To Fifteen Generations https://newrepublic.com/article/116462/family-wealth-lasts-t...
Society doesn't need money. Money is just a tool, and doesn't solve any problems on its own (aside from the inefficiency of barter—but even then you need something to barter first). What society needs—what people need—is consumer goods and services. People who own a great deal of money tend to spend proportionally less of it on consumer goods and services for themselves, and more on capital goods. These capital goods enable more efficient production and thus increase the availability of consumer goods for everyone else. Redistributing wealth is a great way to force consumption of capital, resolving a short-term cash-flow issue by destroying the means of production. You get a gratifying boost to your bank account, but after a brief period there is little on the store shelves on which to spend it.
As for inheritance specifically, I agree that it is fair, in general, to say that the recipient of the inheritance has done little to earn that money. So what? Would you really say that you do not have the right to give someone an unearned gift—that this is not a legitimate way for you to choose to spend the resources you have either earned for yourself or been given by others? Or is it only gifts to one's own children which you feel should be out of bounds?
I can give my family a gift to ease their life.
But it's different from giving them a gift that removes all fincancial problems for their whole life.
Of course, as others have already pointed out, inheriting wealth does not guarantee a life free of all financial difficulties. That depends on how the recipient uses the gift.
Personally, when I'm feeling a bit revolutionary, I find myself favoring Thomas Paine's solution in Agrarian Justice to help fund something like a UBI.
For example, should the president's son, because he's the son of the president, have a special citizenship that allows him a $1m income for the rest of his life? And a Presidential health care card that affords him the base care. And a free pass to any ivy league university, just by virtue of him being the son of the president?
We say no, because we believe in a meritocracy. Through hard work and merit, i.e., your contributions to the rest of society and your hard work, you're afforded access to good schools, good jobs and an income that affords you good care.
But if you inherit $10m, you can skip all that. At a normal 5% ROI, you can live the rest of your life on a $500k salary. You can get access to the best tutors, best schools, best care, and perpetuate your success to the next generation. (the idea of social reproduction).
Money buys you tons of opportunities, access and leisure. By inheriting money, you thereby inherit opportunity, access and leisure. We don't accept that if opportunities (e.g. jobs) or access (e.g. special care) is handed down through a corrupt political system, but we do accept it when it happens indirectly when money is handed down, and this money in turn buys opportunities and access.
Of course there's a balancing act. We want fairness in opportunity and access, but we also want to provide for our kids and leave them better of them your parents left you. We want to set-up our kids with a minimum safety net, and sometimes we want to leave our kids a family business we hand down generation after generation. Somewhere in between there's a level of distributive justice that makes sense, where a minimum amount of inheritance is exempted, after which the remainder is taxed heavily.