Well, the nature of taxation is that the more you earn and pay in the less you tend to get back out, at least directly. Arguably as you get richer you benefit more from law and order (people not taking your wealth) and from mass education and healthcare (providing your business with an educated and healthy workforce).
One of the reasons why pension contributions are mandatory deductions from wages are to make sure everyone pays in at least a minimal amount. Of course some people never earn enough to cover their costs in retirement... Well, you could just throw them out on the street I suppose, if you felt okay about doing that, but then there is a very real danger they will just come and steal your stuff rather than die quietly. I've never really heard a credible plan on this front, other than building very high walls around your home (if you can afford it).
The reality is that the state pension is very low, so if you did provide for yourself you will definitely be a lot better off. Anger and rage at the less fortunate is mis-placed, you should be upset by the bankers and super rich who are the real reason your quality of life isn't better.
The idea that the wealthier benefit more from the taxes paid in the form of more "protection" is absolutely untrue. Our Supreme Court has even ruled that the police do not have an obligation to protect the individual.
Also, the idea that there is a binary choice between "force the people who can afford it to pay for them" and "let them die in the street" is also untrue, and a false choice given by politicians to coerce folks who don't think it through themselves. It is the basis for the ever increasing welfare state we (and certainly you) live in.
The fact is that before we had all this progressive taxation and welfare programs, there were not dead bodies littering the streets, nor did we live in anarchy. People fended for themselves much more so than they do today. I don't think anyone (with any integrity) has a problem helping out those who truly need help, but in the USA (and UK) those that truly need help are a miniscule fraction of all those who are happy to accept help, whether needed or not.
It is human nature to take the path of least resistance. It's inherent in our species to not work for X if you can get X for free. A big part of the problem is that it's so easy to live quite well on 100% social assistance that we're made it uninteresting for people to bother working.
As for retirement - the social security system is already progressive. Those who never earn enough to pay for their retirement are already subsidized by those who earn more. The fact is that more and more are getting more than they are paying in. The reason for that is because people are living longer, and because politicians are loathe to raise taxes on anyone except 'the rich'. So when social security has been paying out for 20 years instead of the anticipated 5-10 years, and when the politicians have raided the coffers, it means there is a huge shortfall. The correct decision is to either raise the age of retirement, or increase the tax rate for social security. That maintains the current fairness and lives up to the promise of what SS was supposed to be. Keeping the tax rates low, telling higher earners "too bad, we promised you will get SS, but we're rescinding that because your money is needed to pay for lower earners we don't want to raise rates for" is unfair and does not live up to the promise of what SS was supposed to do.
The choice seems pretty clear to me. The only reason it's even a debate is because the politicians all want to be the hero of the working man and tell him "the rich" are the ones screwing him over and keeping him from prosperity... and if they'll give said politician their vote, he'll right this wrong.