Thanks for the response guys. It's something I've not given much thought, assuming that training both sides is the only way to go about it. However, I've noticed that during competition I only attack on one side...Thanks again.

That is a major part of his offensive philosophy. When attacking (unlike defending), you can usually choose which side you can attack with. Especially for techniques that require a lot of coordination, he believes that honing your strong side is better than training and using both sides. That way, in competition you will know you always have that extra bit of strength, confidence, or coordination that comes with using that side. There are exceptions, such as his half guard passes where he trains both sides, and he has passes to both sides. However, for many of his attacks you will only see him use one side; attacking the turtle, rear naked choke, north-south choke, guillotine, X-guard, two-on-one hand control, etc.

For techniques requiring a lot of strength, he uses his right side (eg, chokes). For techniques that are more timing or coordination based, he may decide to use his left side, especially if that side is necessary to chain into another favorite technique on the follow.

Not everyone follows this. Some instructors teach you to train both sides so that you can take advantage of someone who gives you an opening for your weak side, or so that you can attack your opponent's weak defending side (assuming you have some data on them). Roger Gracie chokes with both hands, Pablo Popovitch attacks the turtle from both sides, etc.