Any time you go unilateral on an exercise – using only one arm or one leg – you're challenging your ability to control rotation via your core musculature. The angle of pull from the low cable provides constant tension on the biceps while the bilateral stance with unilateral pull challenges your ability to fight rotation.
If you can't use a heavy enough weight to fully challenge your biceps because the weight is twisting you around, work from a split-stance position first – one leg forward, one back.
Think you have what it takes to make it in the world of elite sports? Do you have immense talent and ability? Great, but so do a few thousand other guys. Unfortunately, all of these things will only get you so far in this world where good isn't often good enough. At this level you have to be one of the best just to get your foot in the door.