Overgeneralisation about carbs and their effects on insulin levels is where the myth that carbs are bad for you has come from.
People mistakenly believe that the glycemic index ranks foods by how dangerous they are. The glycemic index is a figure representing the relative ability of a carbohydrate food to increase the level of glucose in the blood.
Insulin helps to regulate your blood sugar levels (glucose) and early evidence suggested that carbohydrates made your body less sensitive to insulin. This can be true for some diabetics and insulin-resistant people who overeat carbs, but the same effect is not seen in healthy people who enjoy a healthy diet. Insulin resistance is developed due to a number of different factors, including poor sleep, physical inactivity, excess fat, and genetics.
Eating less carbs, and especially processed carbs, can cause fat-loss, however, only if you eat less (i.e. you are in a calorie deficit), where the amount of energy you are consuming is slightly lower than what you are expending. Use food diaries/logs and kcal calculators to compare your balance. Try http://www.freeweightloss.com/caclulators/ to calculate your kcal needs then remove 10-15% for a steady fat loss target. Replacing non-protein nutrients with others (fats and carbs) will not see an effect on weight loss but a calorie deficit will.
Keep your protein intake somewhere between 1.6-2g/kg bodyweight and then choose the remaining split of carbs and fat based on personal preference, however, fat should equal no less than 20% of total energy intake to help maintain hormonal health.
Conclusion: There is nothing inherently bad about carbohydrates. Overindulgence is what causes weight gain.