You're not weird, RitaMarie. Although I started out unclipping right, somehow, I switched to the left. Now, I can't even get on my bike from the right side... after 9 years. I really don't know the order I do stuff either. I unclip a little before a stop and I *think* I lean a tiny bit left and forward. Next thing I know, my foot is on the ground. It all happens in like a second.
I have tried unclipping on the right side. While I had no issue actually taking my cleat out of the pedal, I felt like I would fall if I tried to actually put my foot down. I know you are supposed to feel comfortable doing both, but I never bothered to try again. Interestingly, I can unclip and stop on both sides on my mountain bike, mostly because I always am on the alert to stopping due to obstacles (I generally suck at mountain biking).