As long as your body is burning carbohydrates for fuel, it's not burning fat, period.

Insulin only enters your bloodstream after you eat carbohydrates. Insulin is the only hormone that tells your body to burn carbohydrates. There are more than half a dozen other hormones that constantly exert pressure on your body to burn fat, instead. Think about that. The only thing that makes you burn carbs is eating carbs. As long as you're burning carbs, you're not burning fat. That means that eating fat doesn't make you get fat. Let me separate that out so it stands out a bit more:

Eating carbohydrates makes you store fat. Eating fat (and protein) makes you burn fat - which means you get thin.

Insulin resistance causes your body to ignore blood sugar (insulin is what makes your body respond to blood sugar.) The problem is that when you get insulin-resistant, your blood sugar goes WAY over the top of what you need to get by before you make enough insulin to respond properly. At that point, your body does what it always does with extra blood sugar: transforms it into fat and sticks it to your tummy.

Then, when the crash comes (and oh, boy, does it come!), you have to eat even more carbs than last time to get your blood glucose up high enough to get over your insulin resistance, and you pack on even more weight.

The only way to break the cycle is to let the crash come, muddle through it, and start eating fat and protein without carbohydrates. Depending on how many incidental carbs you get in your fruits and veggies, that crash can last from 48 hours (for a total fast), to two weeks (if you still continue to eat normal levels of fruit and a few whole grains.)

That's how long it takes your body to adapt to a low-carb diet by no longer producing insulin in preparation for a meal. But after the crash, you'll find that, because your blood sugar has stabilized (no longer swinging up and down over the day) - you're not as hungry anymore, and you don't feel as slow, shaky, and headachy as your blood sugar drops.