Time to wrap up and move on. Chief, I'll make one last attempt to explain why mconnell got the right answer and gave the right reason. I'm making this non-insignificant effort for you. Please, read carefully.
We'll start from the ideal case and then, once we understand that, we'll move on to include the "real world disturbances" that trouble you so much.
We need two important laws of Physics:
1. Newton's second law of motion says that the acceleration of a body is proportional to the force applied to it. If you want to stop a falling body in a short distance, you need to apply a large force. If you want to go from 0 to 60 in 5 seconds in a big truck you need more torque than in a bike.
2. Hooke's law of elasticity says that the force exerted by a spring is proportional to its stretch. This proportionality law applies to ideal springs, but we'll see that we can use it for non-ideal real ropes too. The reason is that we only need to assume that the force grows with stretch, not that it is exactly proportional, and that is true of real ropes for not too large stretches, which is all we need. The other important observation is that a long rope is a weaker spring than a short rope. Any climber is aware of that.
Our ideal case has no friction and two identical climbers taking completely clean falls at the same non-zero speed. There is only one piece of pro. There is no slack in the rope and the mass of the rope is negligible compared to the mass of the climbers. We ignore air drag and make other reasonable assumptions of that nature. Once again, we review the ideal case because it provides a baseline for the analysis of real falls.
As the climbers fall, the rope goes through the biner connected to the only piece of pro until the leader hits the biner. At this point both climbers start decelerating. Why? Because the rope is "caught" in the biner and opposes their fall. The rope stretches and in so doing applies a force to the climbers.
Suppose for a moment that the rope were locked off at the biner as soon as the leader reaches it. Then, effectively, the leader and the follower would be falling on two separate ropes: one very long, and the other very short. The long rope would give the follower a very soft catch, but the very short rope would produce forces so high that something would probably break.
However, the rope is not magically locked off at the biner. Therefore, in the absence of friction, it stretches uniformly. This means that its tension is uniform, which means that the two identical climbers are decelerated at the same rate. Since their initial speeds are equal, they remain equal. This can only be achieved by rope moving through the biner from the second's side to the first's side, because initially there is no rope of the leader's side.
All right, we made it through the ideal case. We didn't write any equations. Rather, we did a little bit of what in some circles is called Qualitative Physics. We concluded that in the ideal case, the leader is not stopped abruptly, but decelerates at the same rate as the follower. The middle point of the rope does not move. Each half of the rope arrests one climber. Since the rope that arrests the leader is half the rope between the leader and the second, it is as if the fall factor had been doubled. On the other hand, if the leader had fallen from 10 feet above the last pro in pitched climbing, the rope would have come taut after a 20 feet fall, whereas here it comes taut after just 10 feet because the second is "taking in slack."
Let's not get caught in these details, though, because we still have our main task to undertake.
Let us first assume that everything is like before, but there is friction between rope and biner. The effect of friction is that the tension in the rope is no longer the same on the two sides of the biner. However, it cannot be arbitrarily different. Friction can only do so much. Initially, friction is strong enough to prevent slippage of the rope, but as the very strong spring on the leader's side tries to stop him/her in a very short distance, its tension grows very quickly, which creates a large imbalance until the rope slips.
Something must be noted here. We have not made precise assumptions about the forces. Once again, we have resorted to a qualitative argument. The reason why this works is that the rope on the leader's side is initially so short (in fact, we are assuming zero length) that if no rope slipped through the biner, the imbalance would grow enough to exceed friction. Friction is a complex phenomenon, but once again, we don't need the exact value of the friction force.
We have taken care of friction at the top anchor. Let us now look at weight imbalance between the two climbers. With little or no friction at the biner, we know that eventually the heavier climber will pull up the lighter climber all the way to the biner. Suppose the follower is heavier. Does that prevent the lighter leader from falling lower than the biner? No, because the tension on the follower side is now higher, but the tension on the leader side will grow indefinitely unless there is some slippage. Once it has grown large enough, slippage will occur. Eventually, the leader will bounce up, but that's not our current concern.
We account for more than one piece of pro in the same way. Additional pro adds friction. Friction makes it harder for the leader to pull rope to his/her side. However, if no rope slips, tension grows indefinitely. Hence, at some point, some rope will slip. Less rope than in the absence of friction, but still some.
Once we understand the basic argument, we see how to apply it to other factors. For instance, do we need to assume that the two climbers have the same initial speed? Of course not. Hence, the fact that they didn't have clean falls does not trouble us (though it's likely to trouble them).
Did we ever concern ourselves with the specs of the rope (diameter, impact force rating,...)? No, because from the beginning we stipulated to work only with a qualitative version of Hooke's law that makes no distinction between a Mammut Tusk and a Beal Stinger. In sum, our conclusion for the ideal case continues to hold in the real world.