Why did owning land improve a person's status in Ancient Greece?

Owning land only improved a person's status if he owned a sizable chunk of it; otherwise all farmers would have been high-status citizens, which they weren't. The reason is simple really: in a time when there were no Rolexes, yachts, trophy wives, gold and diamond-studded bling (or front teeth) or private airplanes, one of the few ways of showing that you were rich was owning a lot of real estate. And that certainly went in a country like Greece that was mostly densely-forrested mountains and where good land was rare.