A short answer is that it's required by the USGA/RCGA handicap manual, paragraph 3-5. In fact, the USGA and RCGA have ruled that a club cannot choose to ignore paragraph 3-5, because a club cannot choose to ignore any of the Rule of Golf. The best way to explain the rationale for the rule is to use an example:
The course rating for any set of tees is the score a scratch golfer could be expected to shoot from those tees. Your course handicap is the number of strokes that scratch golfer would have to give you in order for you to have a fair match when playing him from the same tees.
So let's say you are playing a scratch golfer, both of you playing from the white tees at El Tigre. Your course handicap from the white tees is 14. We expect the scratch golfer to shoot 70 (69.7 rounded) and you to shoot 84 (69.7 + 14, rounded), and you would tie.
Now let's say the next day you move to the gold tees and the scratch golfer plays from the blue tees. He is again expected to shoot the course rating, which is 71.7, rounded to 72. Your course handicap is again 14, and the course rating from the golds is 67.5. So the scratch golfer is expected to shoot 72, and you're expected to shoot 67.5+14=81.5, rounded to 82. If we didn't adjust anyone's handicap in accordance with paragraph 3-5, your net score would be 68 and you win by 4 strokes. Now if we had adjusted handicaps IAW 3-5, we would have either added 4 strokes to his handicap or deducted 4 strokes from your handicap, because of the 4 stroke difference between the course ratings of the two tees (71.7 - 67.5 = 4.2, rounded to 4), and you would have again tied.