In order to rent, you need to rent from someone. If everyone can own at most two pieces of real property, that means that at most only half the population can rent, because the property owners will live in one home, and will rent out the other (well, sure, some will rent out rooms in their primary residence).

In reality, half of the population will not want to (or be able to) own two properties (and many will not even be able to own one), so you end up with a nominal amount of home ownership, a very tiny rental market, and a bunch of people who both can't afford homes and have nowhere to rent because of the aforementioned very tiny rental market.