surface contact area
I don't know if this is the way it really is, but when looking at the size of the strands of the rope, it seems that smaller strands equals more area at the surface to contact the tree or friction-hitch. If a line contacts an arch (i think this is called a tangent...i don't remember my geometry well enough). In this hypothesis, the strands are the arcs and the tree contacting it is the line (maybe the tangent?) It only contacts in one tiny spot. If there are 24 tiny spots, that would be more friction that 12 or 16.
However, I don't think it's that easy. Being made up of 24 smaller strands, the Fly's profile more closely resembles a circle than it's lower-stranded counterparts. A twelve strand line, when weighted, tends to take on a hexagonal shape. This hexagon might be the part that is coming in contact with the tree. If that is the case, the hexagon would have more surface area than would the circle.
So what's right? There was mention (from Mike Maas & Co.) that I sometimes confuse you guys. This might be one of those times! In this example, it might just be the case that there are so many other factors to consider (the squishyness of the rope, for example) that I might be looking to closely at the rope.
Something to think about while you're eating dinner.
love
nick