The reason why it's hard to burn fat during high intensity exercise is that it's a slow and inefficient process of getting energy to the muscles. Your body will switch to using glycogen aerobically and/or anaerobically.
The infamous "fat-burning zone" concept is highly misleading. It's true that we don't burn a lot of fat during high intensity exercise, but we do burn a lot of calories (in the form of glycogen) that will be replenished later by increased metabolic activity, effectively burning the equivalent amount of fat. Since high intensity exercise burns more calories, at the end of the day, it burns more fat too. But there's a downside to that: you'll feel much more exhausted. The idea behind doing easy to moderate physical activities for weight loss is that if you're getting most of your energy from fat during the exercise, you won't feel as tired during the rest of the day, because your glycogen stores are intact and there's no need for muscle recovery.