Your title is very ageist. It surprises me that you support equality in every other facet of life except for this one thing. The problem isn't with our understanding of Capitalism vs Socialism. The problem is with GOP vs Democrat. All of the political rhetoric supports this binary that compels you to choose a side.
Your post reinforces this divide. You are participating in partisan politics through your entire post. Why not actually talk about applied economic principles instead of describing the existing rhetoric that we can't seem to get past? If we truly want to talk about economic principles over politics, why not start by talking about what belongs in the private and public sector with respect to spill over costs and benefits? Maybe we should discuss what is most effective to be managed by the government, and what should be market driven? I'm personally open to having a reasonable discussion about government spending that is substantive.