Backwards

In his (in)famous article, "The Social Responsibility of Business Is to Increase Its Profits," Milton Friedman argues that businesses are not the sort of thing that can have responsibilities. Only people, says Friedman, have responsibilities.

But why not say that he's got it backwards? One should reason that since people have responsibilities and since businesses are (at least partially) composed of people that businesses have responsibilities, too.

Or at the very least, Friedman should give us an argument that the reasoning should run in the direction he says it does and not the other way around. But he doesn't.