When you step to the left you are punching with your left foot. the left foot just moves, back foot pushes and creates the movement.
When you step to the right you're probably trying to throw with the right foot. Right foot moves, left foot pushes.
You can throw whilst stepping left because it's basically the same as stepping forwards in terms of balance, you can't throw whilst you're moving right because in terms of balance it's basically the same as moving backwards. You have to throw in between the shots, different rhythm and timing.
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