To recap, the claim is that capitalism does not require continual growth, and it requires only private ownership. Actually, it requires both. For more details, view
http://en.wikipedia.org/wiki/CapitalismAgain, note the key points in the first paragraph alone:
- private ownership (actually, private ownership of means of production)
- profit (there's your growth)
- capital accumulation: again, derived from profit, and grows as profit is re-invested in businesses, leading to more production, and with more sales, more profits
- competitive markets: notice the connection between this and more production: in order to compete with other businesses, one has to increase productivity or efficiency, which means lower costs, but because there's a limit to lowering costs, then the only way to compete is to increase production given the same amount of costs, which means
- price system: one can keep prices low (because costs per unit go down) or make more profits per unit sold
Now, why continuous growth? There are many reasons:
1. laborers who want higher wages;
2. investors who want better returns;
3. consumers who want cheaper products;
4. competition;
etc.
Again, note these in light of the key points given above.
Can capitalist economies experience de-growth? Absolutely, given economic crises, but they eventually make up for losses by a return to economic growth. That's why economic growth via increasing money supply, resource consumption, etc., has been growing worldwide in sum and per capita. That's why various economies are also keen on looking at annual GDP growth.