It's not about the space, it is about the environment. You can compare it to living in a small apartment vs. living in a mansion. You will feel much better and be healthier overall if you live in a CLEAN small apartment vs. a FILTHY mansion. The only reason why having a larger tank for beginners is encouraged is because it is very difficult to filthy-up a mansion with one person living in it.
There is a difference between how breeders and pets keep their fish. You honestly cannot expect a breeder, with thousands of fish, to keep them all in 5 gallon tanks...not even 1 gallon cubes.
It's all about keeping the water clean. It's just much easier in a larger, cycled tank.