While I found the exercise nearly impossible at first, I got passed that stage and now routinely practice the essence of exercise about once a week.
In my opinion, the exercise is difficult because it assumes mastery of certain fundamentals which a person might not have developed yet. Here are a few that comes to mind. First is the maintenance of good wrist posture. You want to have the fingers able to position/move parallel to the fret. This minimizes the distance each finger needs to travel and simplifies the task. Second, the strength of the different fingers should be “balanced”. In my case, I had a very weak pinky finger and was unable to complete half of the "independence exercise". My solution to the problem was to practice a lot of ascending/descend slurs (i.e., hammer-on and pull-off) until each finger functioned similarly. Third, one needs to develop "opposing finger motion". Without acquiring this skill, the pair of fingers either won’t switch or won’t land simultaneously on the strings. Opposing motion can be develop using other exercises listed in the book. One exercise concerns the opposing motion of neighboring fingers 1-2, 2-3, and 3-4. The other two exercises (i.e., the “spider” and Odair’s) concern other opposing finger combinations and are also worth mastering.
After I acquired the above skills, the finger independence exercise became much more manageable for me. Hope this helps.