Here is the reason why. Your body needs a certain amount of calories to maintain its lean muscle mass. When you go on these low calorie diets you DO lose weight but you are not only losing fat. You are losing fat and muscle. This is a big problem, because the more muscle you have the more fat you burn.
So lets say you go on this type of diet for 30 days. Most people can't stick to them for much longer than that. Lets say that best case scenario, you lose 30 pounds (5 pounds of water, 15 pounds of fat, and 10 pounds of lean tissue). Then you go off the diet and now you have 10 pounds less of lean tissue, which burns fat, you gain 10 pounds back almost immediately and those pounds are fat pounds. Now you are actually a higher percentage of fat then you were when you started. So while you might be a few pounds lighter, you are actually fatter! It is also virtually impossible to meet your nutritional needs for carbs, protein, fat and fiber while eating 500 calories. It is also highly likely that you will be deficient in your vitamins and minerals. These crash type diets lower your metabolism because it does not give your body enough calories to fuel it. Compare your body to a car; if you don't put gas in the engine then it won't be very efficient.
This article found on cardiopump.com puts it well and explains the science in layman's terms:
"It’s easy to understand why this phenomenon occurs when you understand the science behind body fat. When you gain weight, your fat cells expand. A fat cell is able to grow to about three times its normal size before dividing. There is no limit to the amount of times a fat cell can divide; it is not able to swell greater than about three times its normal size so as long as you continue to gorge excess calories into your mouth, your fat cells will continue to grow in numbers. Once you have new fat cells, they are there for life. The only known way to get rid of the cells is through liposuction. That’s not to say that after you have these additional new fat cells taking residence in your body that you will forever be overweight. Weight loss is not the reduction of fat cells, but rather the shrinkage of them. Like taking water out of a water balloon, that is what happens when you create a caloric deficit (either through diet, exercise, or both). The body fat stored in the cells will be metabolized out of the body. (I am often asked what happens to the weight? Where does it go? Well, it is excreted through sweat, urine, and carbon dioxide that you expire from your breath). Like a water balloon shrinks down to a flat, flimsy piece of empty balloon when you open the hole and pour out the water, same thing happens with your fat cells when you lose weight. However, that balloon is still fully capable of expanding again if you put the opening back on a faucet and fill it up again. Same goes with your fat cells. They are still sitting in your body like limp balloons, ready and able to swell if you allow caloric intake to outnumber caloric expenditure. This gets me back to why yo-yo dieting makes it difficult to keep weight off permanently. The more fat cells you have, the greater potential you have for gaining weight: the cells already exist so all they need is the calories to plump themselves up again. It’s easier to lose weight and keep it off if the number of fat cells in your body is less. So, instead of jumping on the next fad diet to lose weight quick, and setting yourself up for a feast fest that is sure to fill up your fat cells, multiply them, and leave you in an uphill battle when it comes to achieving a healthy physique long-term."
Hate to break it to you but there is no magic pill, there is no magic diet! In the past I have tried these techniques only to fail miserably. Many of these diets have been around for over 50 years, if they worked...everyone would do them and we wouldn't all be so obese. The only way to lose weight and to do it in a healthy manner is to make lifestyle changes and reduce your calories and become more active. Trust me, I know how hard it is, I know how frustrating it can be when you look at the scale week after week with no results. I want there to be a magic pill; I do... and maybe someday there will be something but for now stay away from all these fad diets and crazy unhealthy low calorie plans. You'll just end up fatter later.
Not trying to offend anyone. These are just my opinions. If you are currently participating in any of the diets listed...best of luck to you...I truly do wish you the best :)