Another fine example of reverse psychology for you, christopher. See, not only LP uses it on horses.
regardless of that, it defies parelli's principle of "maintain direction" (true straightness) being priority 2, and his method of achieving that.
"maintain direction" can't be achieved by saying "left = more left". because the pattern will tell the horse that when it wants to go left, it should go more left.
maintain direction is achieved by "left = right" in equal measures. that way when the horse wants to go left, it will also go right in an equal amount, resulting in the horse staying straight.
the reason i teach the horse to go more in the opposing direction is because when the horse deviated it tells me the horse isn't even in the first place, so straightness no longer is the priority, evenness in left/right is the new priority. because evenness in left/right results in straightness.
i dont know how i can make this any simpler :s
i suppose an easy way of saying it is, if the horse were to make a 5 degree turn to the left, rider should from there take a 10 degree turn to the right. 5 degrees to get back to the straight, and another 5 degrees because straight lines aren't the issue, evenness in left/right is the issue, and the horse turning 5 to the left in the first place told us exactly how uneven the horse is, and exactly how much we have to do to solve it.