Unknown. A common element for many cases of appendicitis is obstruction of the opening, through which it connects with the rest of the intestinal tract(we often find stone-like material upstream from rupture points);however, this is not a universal finding nor do we understand why these appendicoliths form. My guess is that there are many factors that contribute to it developing considering how common it is.
Another possibility. Other people theorize that there are nests of lymphatic cells that make up your immune system. When this lymphatic tissue gets active, it may swell, and obstruct the appendix in a similar way to what dr. Rosen described.