Well, you've done the Ayn Randian thing here, and distilled a very complex issue into two different polarizing viewpoints.
Saying that I, or the previous commenter whom I mostly agree with, "would gladly have [our] opinions and preferences imposed [our] neighbours with the threat of force" is wrong, and not very conducive to debate. To say that we "want the gun to solve society's ills" is even more so.
Democracy is supposed to be a grand discussion. I can't have my opinions forced on others, we all have to talk and come to an agreement on how things should be done. So, thinks like jury duty and social security were put into place to attempt to solve problems like "how can we best determine if someone is guilty of a crime?" and "what can we do about old people who have worked their whole lives but are reduced to eating cat food because they have no money and no real ability to make more?"
Now, ideally, these decisions could be made by consensus. Every single person in the country could agree on the right way to do things. But, having participated in a consensus based community for a number of years, I can tell you that it does not scale. So instead, majority rules (with checks and balances, in the US). My understanding is that your viewpoint would be that, while we can all discuss possible solutions to these problems and work on making our country a better place together, no individual should be coerced into supporting the solutions. I certainly see a lot of merit in this view. It seems fundamentally fair and respectful of personal freedoms in a way that our current democracy perhaps doesn't. However, I see it as less fair than our current system in other, important, ways.
Mainly, it is difficult to separate out the ways in which governmental programs benefit you in a useful way that would allow people to not receive some of those benefits. We are all benefited by not having poor people, young and old, dying in our streets. It seems fair to me to say "if you want to be a part of our community, you have to play by our rules" What should be great about democracy as compared to many other forms of government, is that by becoming a part of a community, you are given a path to be a part of shaping those rules.
This is long, so I will stop. I'm still very much in the process of working out what I think about all of this, in fact, writing it here was helpful for me. I'd love to hear what you think.