The the induction phase gets people used to losing weight at a fast rate, which will not last and is not healthy. Faster weight loss does not mean healthy weight loss. Any diet that emphasizes fast, easy weight loss is one to approach with caution. The guidelines are clear that a safe, healthy rate of weight loss is to lose 1 to 2 pounds per week after the first couple of weeks. The Atkins diet states you will lose "only body fat" by eating regular meals, taking in adequate calories, and keeping your insulin levels down. There is no way to only lose body fat when losing weight. Each pound you gain from consuming excess calories is 75% fat and 25% muscle, and each pound you lose from cutting back 3,500 calories is the same ratio of fat and muscle. Claims that you will lose only fat are not based on science despite the fact that the Atkins diet claims to be scientifically based.
Also, she promotes heavily processed items like fake butter and mayonnaise, even (although she doesn't overly encourage it) phony hot dogs. She never mentions coconut oil, which surprises me because it's so hyped as a health food, as necessary fats and good for you. It can be used in place of butter or oils (she promotes saffron oil a lot, which I don't know much about).