The "carbohydrate-insulin hypothesis" is the idea that carbs cause obesity because of their ability to increase the hormone insulin. But in reality, calories control body weight, not insulin levels.
This has been shown in research comparing high and low-carb diets. If a high-carb/low-fat diet is compared to a low-carb/high-fat diet where calories and protein are equal, the effect on body weight will be the same despite low-carb dieters having lower insulin levels!
Weight loss is clearly dependent on calories rather than insulin levels, so when calories are controlled (as they are on the Avatar system), eating more carbs will not impede fat loss.
On that note, if you’re just starting with Avatar and are switching from a low-carb to higher carb diet, you may experience a slight jump in scale weight due to fluid-retention. This fluid retention is caused by an increase in glycogen (stored carbs) and a temporary shift in sodium levels (due to increased insulin). Not to worry though, the increase in weight isn’t caused by fat gain and should level out within a week or two.