That is simply a function of physiology. Most players are right handed, and it is easier for right handers to throw passes right to left.
What separates the good teams from the rest is to have a right side attack that is effective enough to ensure the defence doesn't load up on one side and if they do - punish it.
Yep the passing is usually better to the left and as a result most coaches put their best weapons on that side so it becomes even more pronounced. But our right side is going pretty well, well enough to keep them honest.