I've been there. You hear your whole life that the formula to losing weight is simply burning more calories than you take in, so it seems that the logical next step would be to take in as few calories as possible. If you don't eat, you don't have to worry about the calories in part and you'll be on a calorie burning deficit.
What that formula fails to cover is that eating healthy, much like in math, is not a cut and dry formula. In math there are things called polynomials. A polynomial is a mathematical expression that includes constants and variables. Some things (like calories in vs. calories out) are constants...meaning that always holds true. But there are also variables to consider. These variables affect how the calorie burning/weight loss process works. A few variables to consider when trying to lose weight are things like stress, hormones, water intake, metabolism, and the amount and type of exercises you are doing are just a few variables.
When we deprive ourselves of food and don't eat enough, some of these variables begin to sabotage the original calorie in/calorie out formula. First, when we don't eat enough, our metabolism slows down. And when this happens, we burn fewer calories than we would if we were eating sensible meals and snacks. Secondly, when you deprive yourself, you deprive yourself of the energy that you need in order to get adequate exercise. And as we all know, a lack of exercise = slower weight loss results.
Perhaps the most compelling reason I've found to not starve yourself is the realization that it is during times of deprivation when Satan is most likely to rear his sneaky, ugly head and try to get you to overindulge your flesh and thwart your best laid plans. Think about it. When did Satan directly tempt Jesus? When he was in the wilderness fasting. Satan knew when Jesus would be at his weakest. When did the Israelites grumble and complain the most about God? When they were in the desert. They hadn't had food and they had all but forgotten all that God had just done to free them from slavery.
The same holds true with other things too...it's not just food. If we mismanage our money and are broke, we are more likely to get money via means that aren't ethical or sometimes even legal. Men may be more likely to turn to pornography if they feel lonely or rejected. Women may be more likely to look for solace in the arms of another man if she feels like she is being deprived of understanding. We feel empty and unfulfilled and Satan uses those feelings to push us toward something (anything) other than God to try and fill those longings.
If you can't see the physical disadvantages caused by depriving yourself of healthy food, then at least take note of the spiritual ones. Unless you are intentionally fasting for spiritual purposes (which is a whole separate post altogether), keep yourself in that healthy place of moderation. One extreme or the other will only lead to more failure and heartache down the line.
“In the desert they longed for food. In that dry and empty land they put God to the test.” Psalm 106:14