The problem with political ideologies, and that includes socialism and libertarianism, is that they base their arguments on ill-defined and messy terms and then at the end they pop out suspiciously clean and elegant conclusions.
This is precisely the problem, thank you for defining it.
The human language is incapable of capturing the complexities of the real world.
This is only the case as long as words have no definition or meaning. Until then no intellectual discussion is possible. When words have a clearly defined meaning, then arguments based on logic and reason become possible.
One of core values of socialism is that the rich have a moral obligation to redistribute some of their wealth to the poor.
For the sake of argument, I am going to call this "socialism", as you did. Some may disagree on what "socialism" means, but lets just agree on what the above sentence means.
Then there are people who support an ideology which does not share this view of "moral obligation". I called them "libertarians" in order to make a distinction between the two groups. Now people will say that's not what "libertarian" means. Fine. Ayn Rand called her philosophy Objectivism, so I will use that in place of Libertarianism, if that helps.