Mike, this is a really large and complex subject, about which I have written two books and many articles, so I cannot hope to give an adequate reply in a blog post. Do read Marx's CAPITAL, volume One, at least the first eleven chapters or so.
Now, about those coconuts. This little story is what Marx called, rather charmingly, a "Robinsonade," meaning by that a fairy tale a la Robinson Crusoe [the protagonist of Daniel DeFoe's famous novel.] This is exactly the wrong way to think about capitalism. The right way, as Marx shows in CAPITAL [and following the lead of Adam Smith in this regard] is to study its historical growth and development. Briefly, Marx argues, what happened in England [and elsewhere] was that the peasant farmers were displaced from the land on which they had gotten their living, and forced to migrate to the cities, where, without any access to or ownership of the means of production [land, forests, mines, rivers, tools, etc], they had no choice but to sell their labor as factory workers. At the same time, production for use -- growing food to eat, making clothes to wear, etc -- was replaced by commodity production, which is to say production of things that could be sold at a profit in a market. Those who had taken control of the means of production were in a position to force down the wages of the workers, and regularly took for themselves ["appropriated"] the surplus, or profit, left over after they had paid for their inputs [including labor] and sold the commodities that the workers had made by their labor. Over time, the owners or controllers of capital grew richer and richer, while the workers were forced to keep struggling to stay alive. The workers were only able to raise their wages and live better when there was, for a time, a shortage of labor, or by organizing into labor unions and forcing the employers to raise wages and shorten the working hours.
This, not a fable about desert islands and coconuts, is the real story of capitalism, and it may help you to begin to understand what I find objectionable about it.