You're normal.
There is no perfect symmetry in form or function. Ever look at facial halves mirrored (left half face + mirror image of left half face vs mirror image of right half face + right half face eg Here's What Faces Would Look Like If They Were Perfectly Symmetrical)? Your rubbery bits aren't symmetrical, nor are your bones or muscles. No boobs are perfect matches. Or ears. On tope of this, consider that you have a dominant eye, dominant hand, dominant leg. One hand holds the jar, the other opens the jar. You probably do this the same way nearly all of the time.
Barbell training with both sides -- squat, press, deadlift, clean, press -- forces both sides to work together and pushes them toward symmetry.