Your body contains proteins and other structures that constantly become dysfunctional or die. This isn't a bad thing; it's a necessary process for optimal health. However, if these dead tissues aren't cleared out from the body, they can cause cell death, contribute to poor cell and organ function and even become cancerous. Enter a process called autophagy.
There are MUCH bigger fish to fry with regards to getting healthy than a few calories here and there during a fast. 80% adherence that you stick with for a year is better than 100% adherence that you abandon after a month because it was too restrictive. If you’re trying to get to a minimum bodyfat percentage, you’ll need to be more strict – until then, however, do what allows you to stay compliant!
When you eat a meal, your body spends a few hours processing that food, burning what it can from what you just consumed.  Because it has all of this readily-available, easy to burn energy (thanks to the food you ate), your body will choose to use that as energy rather than the fat you have stored.  This is especially true if you just consumed carbohydrates/sugar, as your body prefers to burn sugar as energy before any other source.