> Not everyone equals public healthcare with socialism.

I don't understand your assertion. Why would anyone do that, and what would they call public healthcare instead? Even social-democracy has socialism as one of its components.

Socialism is about distribution of wealth. This is mainly about distribution of risk. It is also a more fundamental thing than creating a more equal society. It is also simply a fact that many people outside US don't call their country socialist just because they have a public healthcare system. So this might cause confusion.