This post makes it a bit too simple. I'm not exactly sure what you mean by 'fat storage mode' but suggesting that insulin resistance leads to overweight is a bit backward. Overweight generally causes insulin resistance, which can eventually result in type II diabetes. High carbohydrate intake has been linked with insulin resistance, but it is hardly the only cause, nor is it clear that it is the only cause.
There are plenty of ways to encourage mobilization of fat. Reducing carbohydrate intake to induce a ketotic state is one of them,
exercise is another.
This assumes that at the time you are exercising your blood sugar is normal. If you have just pounded carbs and go work out. You won't likely be mobilizing much fat.
But in general, any kind of
theoretical calorie deficit is going to result in calories lost, (hopefully) mostly from fat.
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Yes in theory calories in < calories out should result in weight loss....but...IT DOESN'T. When they measure calories in food they use a bomb calorimeter which is a closed system that effectively burns the food(fuel) at the same rate. The human body isn't a closed system and I wouldn't say everyone burns the food(fuel) at the same constant rate or we wouldn't be having this discussion.
Reducing your carb intake doesn't so much "train yoru body to become insulin sensitive" as much as it reduces the total amount of insulin your body needs to release to maintain your blood sugar. I am not aware that low-carbohydrate diets actually reverse insulin resistance itself. Weight loss/exercise decreases insulin resistance because even with the same amount of insulin produced by the pancreas there are fewer cells competing for it, and exercise increases the number of receptors expressed.
Yes and no. People that yo-yo diet are the perfect example... Periods of binging then fasting have devastated their metabolism and insulin response so drastically that it would require a very strict low carb diet to ever recover from their Insulin resistance.