Why is there a double filter? Why must it come apart for cleaning?

The double filter allows for staged filtering - a slightly coarser filter in the lower (basket-shaped) filter separates the majority of the grinds from the dissolved solids.  The upper (disk-shaped) filter completes the job, with a much finer mesh than in any other press.  The result is the ultra-clean coffee, with cleanliness of a vacuum-brewer and the ease-of-operation of a french-press!