> Capitalism is the natural product of freedom.

This is true in the sense that it is the natural products of a very specific conception of property rights that was advanced by the commercial class (they became the capitalist class) for their own benefit, and for which, several centuries after the model began becoming dominant in Western Europe “natural rights” justifications were concocted.

> It is not a designed system, it is an emergent system.

It wasn't “designed” in the sense of deep theory and engineering, and it is “emergent” in the sense that it is a product of individual advantage seeking by members of a particular social group.

You are thinking of markets. Capitalism requires the state. Property rights do not enforce themselves.

These days sloppy use of the word capitalism by both its proponents and critics means that colloquially capitalism == free markets, vs "the acquisition of capital as its own virtue"