Depends on what kind of society you want. Socialism isn't really what you prefer, I hear. In fact, most americans seem allergic to it because they don't want to give money to people not as successful as them, regardless of reasons. But it is a research fact that a more equal society is the best one. How to achieve that if we only care about ourselves in this world? Poor get poorer, and rich get richer isn't the answer.
I think most middle class Americans that don't want to tax the rich, or want a flat tax, like the single father with two kids in this thread that makes approx $36K per year, actually realistically think they will become rich. They think that they (the middle or poorer class) will eventually be in the position of being taxed more than those making less than them. It's a pipe dream, most people will never break out of their economic class. Unfortunately, it's a pipe dream that seems to fuel a lot of the opposition to more progressive tax policy - paradoxically - even if that tax policy will help them for the rest of their middle class lives.
Even if you object to higher taxes for higher earners on principle, another point that seems to get missed with all this discussion is the fact that wealthy people don't make their fortunes in isolation. The wealth accumulated by the rich would not be possible without the society we live in and the associated infrastructure we have created. If we take the example of Apple:
-The planes that hold shipments of iPhones need air traffic controllers, FAA regulations for safety and security, airports strips and crews
-The trucks that hold shipments of iPhones need gas stations, roads, bridges, tunnels, traffic lights, and an educated workforce for those areas
-The stores that hold stock need police protection, insurance companies, water, electricity, workforce, etc.
-The CUSTOMERS that Apple relies on for their profits require disposable income, education, electricity, etc
In essence, Apple cannot simply take from society without giving back their fair share. That fair share is certainly going to be higher than the fair share of the average single person. How anyone could think a flat tax is fair really needs to have their head examined. Apple uses far far more of society's resources to make their profits than any one person - and so accordingly pays a higher percentage per dollar made. Just because they do so on a massive scale, and thus pay a vast sum in absolute terms, should not in any way reduce their tax responsibility.
Lastly, putting some kind of flat tax on income would actually decrease the profits for big business. A flat tax means a greater percentage lost for middle and low earners (Apple's major customer base), and thus less money available for discretionary spending, and thus less money for Apple. Higher taxes for higher earners is really the only viable model as they use more of our shared resources to gain their profits.