Noobman's right. Everyone, including the professionals, has a dominant side. Overcoming it is one of the challenges of becoming a fluid, well rounded player. Even when you have overcome it, you will still always have a side you prefer, but being able to do everything with (near) equal efficiency is the aim.
For me personally, I like taking my tight turns on the backhand (might just be because I worked on my backhand obsessively when I was young), but you can't really tell the difference between my dominant and weak side except for the fact that I clearly prefer going counter-clockwise in my backwards cross-overs. I had two left ankle surgeries by the time I finished my college hockey days and feel precarious going clockwise backwards. Occasionally (very rarely) I'll lose an edge when all my weight is on that left ankle at top speed going forward as well, but for the most part, my skating is and always has been the strongest aspect of my game. Front wise, I can't tell you which way I prefer anymore. I've done so many thousands of russian/circle drills going both ways with a puck over the years that I just don't know anymore. I guess I prefer being on my backhand here as well.
I actually prefer to shoot off "the wrong" foot though. Most right handed shots like to shoot across their body and transfer their weight into the left foot, but sometime after my first surgery, I started shooting off my right foot on the rush a lot and actually, as I got better and better at it, I find that it's a bit deceptive for the goalies and your release can be a lot quicker this way.
