I agree that this rule is completely nuts-o.
To my knowledge, this is the only time where they decided to insert a mechanic for allowing attacks WHILE moving, instead of before, after, or between.
Every other instance of moving while attacking involves either moving then attacking, attacking then moving, or in certain situations, moving, attacking, and moving again.
I believe what these mounted rules are TRYING to accomplish is the following:
A round lasts 6 seconds. You have a mounted archer (A), and a mounted swordsman (S), and their targets (T). The distance between them measured in -. Assume each attacker normally gets 3 attacks.
T - - - - - - - - - - A
T - - - - - - - - - - S
Now, both riders charge towards their target. Over the course of 6 seconds, A is allowed to fire arrows WHILE riding his horse. This means that over the course of 6 seconds, he can continuously attack. S, however, must spend a good portion of his time NOT attacking. Thus, when he gets next to his opponent, he doesn't have a full 6 seconds to swing his sword 3 times.
X represents when the riders attack the target.
T - - X - - X - - X - A
T X - - - - - - - - - S
The mechanic of using the "halfway" point for A is simply for convenience's sake. He's meant to be firing multiple arrows as he rides. IMO, this is broken, and doesn't make any sense, especially when part of your movement might be OUT of range of the target, for things like throwing weapons that don't go too far.