One side of your body is better than the other
Now I don't mean that one side of your body is better from an aesthetic standpoint (although you may beg to differ), but rather that when you are training unilateral movements, one side will almost always be more proficient than the other. This becomes especially prominent in training Kettlebell Sport, where many athletes find they are more efficient and thus can last longer on one side during the Long Cycle, Jerk, and/or Snatch events.
In fact, if you are competing in a Girevoy Sport style kettlebell competition (one switch in 10 minutes), there is no reason at all why you can't go longer on your stronger side. When I earned my silver medal at the IUKL World Championships in 2013, I snatched the 16kg for six minutes on my right and four minutes on my left.
It's normal to be uneven, and in competition you should utilize your strengths to get the most repetitions possible. Since we are aiming for maximal efficiency, however, the goal is to match up the two sides. Therefore, I believe you should always work to reduce the discrepancy between your two sides in training.
What can you do? Well, first of all, you need to be aware of what exactly the inefficiency is on your weak side. Second, you drill to correct that inefficiency in your warm up, using how the movement feels on your strong side as a cue for how you want the weaker side to feel. Third, be patient with yourself - you've been training your strong side how to do everything your entire life, and you can't expect the weaker side to catch up in just a few months, or even years.
Here is a video comparing my right and left side on Jerk. I am using a 28kg bell because the heavier the weight, the easier mistakes are to see! You can see that my right side is fast and efficient, my hips launch the bell, and my heels hit the ground at the exact moment that my arm is locked out overhead. On the left side, my hip does not launch quite as fast, and the timing is off - I am pressing the bell just a bit at the top because my arm is not completely straight in the second dip.
Do you have a discrepancy in repetitions between your left and right sides? Is it more prominent in Long Cycle, Jerk or Snatch? What do you do to correct that discrepancy?