Capitalism succeeds, but why?

In my experience with speaking to people on the Left and Right, many free market arguments are unconvincing and fail to persuade because they lack a conceptual explanation for why is it exactly that capitalism succeeds, and why is it that socialism fails. It is not sufficient to point to the material prosperity of capitalism, or the poverty of socialism, and simply claim that “capitalism is better, that's why we should have that”. That would be a correct empirical observation but does not tell us how exactly we should go about implementing it.

Without the answer to that question, most libertarians, classical liberals and free market conservatives are simply strung along by the political wind-sails and popular rhetoric of the day, without being able to properly assess economic policies and tell if their advocacy for political candidates or policies are consistent or inconsistent with market principles. And this is why the socialist calculation debate of the 1920s, and the fundamental insights from Mises and Hayek, remains ever so important to revisit over and over.

Property rights and contracts are the institutional explanation. Its never really just capitalism. It is private property from Mises on, and more recently, economic freedom. It seems there's always a very clear explanation why capitalism improves material prosperity.

Also Romer on endogenous growth etc.