Have you ever heard someone say, "I have so much trouble going to the right!" You may have said this your self or have heard a friend say this in regards to playing basketball or soccer to name just a few examples. In one regard you can use this to your advantage. But, what if you are the person saying this? What if you could improve this so this doesn't have to be you?
Often times the problem is a weakness in one of your muscles. Cutting from right to left takes a lot of outer hip strength. In order to push off your right foot and move to the left side of the court or field, you have to have adequate strength. Many times having a stronger side comes out of habit and comfort. As a result this habit and comfort turns into greater strength on that side. Solution: try to get the strength on the other side and in turn will result in more comfort.
The other perk to this is better performance. If you can change directions equally to both sides you have an advantage over your opponent. Take for example the image. If Allen Iverson can crossover to the right but his opponent has trouble going to his left then he is in trouble as noted by the picture. But if you are in his shoes and your right hip is as strong as your left, you can easily get in his way and play better defense.
The other problem you can face if you don't have this balance is risk of injury. If you have trouble moving to the left side of the court you will still get there. But what happens is that your body will compensate and overuse muscles or joints not necessarily meant for that change in direction task. Therefore making sure that you have even strength on both sides and even comfort level is an important factor in improving your performance and preventing injury.