I think for me, it is muscle memory. I could retrain myself, but like Aggie, anything that smacks of mechanical or a combination of mechanical and eye-hand is really hard for me. That's why I have always done well in "individual" sports, as team sports seem to require coordination I don't have.
I am right handed, but, I am definitely stronger on my left side. I always hold my coffee cup in my left hand, kick with my left foot. In yoga, I am always the one who wants to start the pose on my left side... so I pay close attention, to make sure I am in synch with the rest of the class.
As I have said before, if my former gym teachers could see me now, they would not believe it. Getting certified to teach aerobics was probably the biggest confidence builder in my life... more than any "professional" achievement, getting my master's degree. Same thing for leading bike rides. I might not be the fastest, but I have skills that I can teach others. OK, totally getting off topic here.
Actually, I had very little trouble learning to use clipless pedals.