To understand why, you'd have to research the subject a lot more on your own. I've given your some hints already. Think. Acne is an immune reaction, and it would obviously go away for a while when you suppress your immune system with something. Then it gets back, and again and again, until you deal with the underlying cause, which is nutrition.
And low carb means a lot less carbs than you could've eaten (i.e., less than 50gr a day).