In the current capitalist system any property that you can get from trade is legimitate, and there is no cap on what percentage of the world you can own. But imagine in the distant future, let's say that one person owns the entire world, his ancestors having accumulated it through normal business operations and trade. The rest of the world's 6 billion people own essentially nothing in comparison and their labor is exchanged in order for them to get the food they need. Is this fair? Should that be allowed? I'm guessing that everyone would say that this is not acceptable. And if you don't, you probably would say it's unacceptable if you were actually living in that situation. Okay, well what about if 2 people owned the world, each owning roughly 1/2 of it? Still no? Okay, 3 people, each a 1/3? No? 4 people, each a 1/4? No? At what point do you say "yes", and how do you justify that decision? In many ways this reminds me of the famous Stephen Roberts quote
I contend we are both atheists, I just believe in one fewer god than you do
We both agree that a certain group of people owning the entire earth is wrong, we just differ on how small that group of people is before it becomes wrong. I believe that the world shouldn't be up for sale, or equivalently, that it belongs to everyone equally.
Perhaps you're sympathetic with that argument. However, you may still feel that by taking away the idea of private property that we are somehow stealing from those who currently claim rights over it. You may feel like they have some sort of more natural, legitimate right to it and what gives society the right to take it away? To this I say, what does "own" really mean? Ownership is purely a social construct. We can't take a test tube of dirt into a lab, run some tests, and prove that it belongs to Mr. So and So. If society decides that no one can own the world, it's as simple as that. You just can't. The notion of ownership just doesn't exist. An example that you can see of this idea today is the air. Air is made up of atoms just like the earth is, yet it can't be owned. Ownership of the air is just something that doesn't exist in our society. Perhaps this is solely due to the practical difficulty of prosecuting air "trespassers", but if it suddently became feasible to do so, I'm sure you would agree that society shouldn't allow the private ownership of air. I believe the same statements can be equally applied to water.
Land is just as necessary for life as air or water. And no matter how lazy our ancestors were, or how bad their businesses fared, or how unlucky they were, should that make us forfit our rights as people to the natural resources of the planet. The planet should not be for sale.