It actually is. Capitalism is defined by the ownership of private property and individuals selling their labor to these owners in the form of a wage/salary, whereas socialism is where private property has been abolished for some form of common ownership. They are mutually exclusive. Social democracies aren't socialist, they're strong welfare in a capitalist system.
So why did the Soviet Union have private housing (and the ability to inherit it)? Why does the modern USA have public lands, managed by the government for the free use of all? How do you classify Chinese communism?
It really isn't an either/or proposition; you're only taking the absolute extremes of the concepts. If it was such a proposition, where does the switch take place? At what point would a nation 'flip' from being 'socialist' to being 'capitalist'?