There are many arguments in favor of progressive taxes, some more obvious than others. A common one is that the accumulation of great wealth tends to lead to power and influence over policy, which in turns leads to more wealth. Wealth begets wealth, the rich get richer. Progressive income taxes are a way of fending of an aristocracy where a few individuals wield incredible power over everyone else. At points in US history, for example, there were individuals who wielded almost as much power and influence as the entire US government.
A related argument in favor of progressive income taxes is that they reduce inequality. Inequality has become a hot topic recently, with some claiming that inequality breeds societal ills and still others claiming that vast inequality is morally wrong regardless of whether or not it breeds other social problems.
But it's the less obvious arguments that interest me here, and they are at least as important if not more. First, let's consider the question "Who benefits most from government?" In theory, governments serve everybody, but not necessarily equally. Our first intuition might be that the poor benefit the most, as governments often institute some sort of social safety net including welfare. But the services and protections of government are actually enjoyed disproportionately by the wealthy, the benefits increasing as wealth increases. Why? One reason is that as wealth increases, so do assets. And the enjoyment of private assets is only possible through government-enforced laws. The Trouble with Billionaires, a recent book co-written by a tax lawyer and a journalist, describes the situation by responding to critics of progressive income tax who decry the "interfering state":
On the contrary, that interfering state has been their best friend. Without it, they'd be scrounging around in the bush with the rest of us, worried about when the next marauding gang was going to pounce on the buffalo they had just speared in an attempt to feed their children. Only with the complex set of laws governing property, inheritance, contracts, banking, stock exchanges, and other commercial relations--not to mention criminal prosecution of those trying to seize their buffalo--can the rich be secure in holding their possessions and enjoy the comfortable lives that come with those possessions.
Besides protection of assets, also discussed here, I would add political influence as a way that the wealthy disproportionately benefit from government. The more wealth you have, the more influence and lobbying power you have, and the more you help control the environment in which you live. So another way of answering this question is to rephrase it and ask "If government is removed, who has the most to lose?" The answer becomes even clearer.
The second point is to consider how the wealth is generated in the first place. There is a tendency, particularly strong in the US, to think of wealthy individuals as "self-made," pulling themselves up by their boot-straps and making billions out of thin air. Of course, you can't actually make billions on a desert island. You make billions by taking advantage of a common inheritance of knowledge and advances, incrementally building upon developments that go back hundreds of years. You generate wealth by drawing on this "common treasury," incurring debts along the way. Taxes are one way that we recognize the roles society and cultural inheritance play in wealth generation.
Strangely, for some people who have achieved great success and wealth that comes with it, they don't feel thankful or lucky or indebted to the society and circumstances that allowed their success, but rather feel that the society owes them. They perceive themselves as self-made men and the majority of others as leeches, leading to such Randian notions as the elite Going Galt.
Thankfully, not all wealthy individuals feel that way. Warren Buffet is a great example. He often talks about how he generated his billions by being fortunate enough to live in a particular place at a particular time where his skill-set (he's good at allocating money in the market) happened to be highly valued. I've referred before to his description of The Ovarian Lottery in determining our fates. It's no coincidence that he favors progressive taxes. He has actually criticized the US government for not taxing him more.
If you're interested in these issues, I highly recommmend this book.