Paying taxes is not a sign that you’re living in a socialist country.
Everyone, except for anarchists, believes that the government has certain responsibilities and these responsibilities require funding which has to come from taxes (of some form). For the most part people’s beliefs about what role the government plays tends to fall into several categories, but the two that have the most relevance to this discussion are the government’s role in "Social" issues and the government’s role in "Economic" issues.
In most cases, when people are describing Socialism they’re talking about a movement which seeks to promote "Social" and "Economic" equality through heavy government intervention. Now, although the principle seems very noble on the surface the reason it becomes so controversial is because of what is meant by "Equality." After all most capitalist democracies are based on the equality of all people.
Now, most people believe in equality but people who promote socialism believe in "Equality of outcomes" whereas people who oppose socialism believe in "Equality of opportunity." The distinction between the two ideals generally surrounds to what extent people should be rewarded or to face the consequences of their actions.
Now, the argument about who fund healthcare is (generally speaking) moronic because (directly or indirectly) you will pay for your own healthcare (through cash, or lower economic growth and opportunity); and the core problem with healthcare is that it has become far too expensive because people are living far less healthy than they ever have before. Whether you want to accept it or not, as long as we continue to spend tens of thousands of dollars trying to cure diseases that are easily prevented (in most cases) health care will not be available for a large portion of people; in a free-market system it will be too expensive for a lot of people, while in a universal healthcare system it will be unavailable because the system will be too strained.
