The HCG diet is not the only one that advocates skipping breakfast. I did a few long rounds of HCG diet when I was initially working on weight loss. Most of the time, I felt perfectly normal. Since then, I have spent a lot of time researching intermittent fasting, which often means skipping breakfast.
When your body is in carb-metabolism mode, eating more frequently and not skipping breakfast is VERY important to maintain energy levels. Carb metabolism is a series of blood sugar increases followed by insulin releases and then blood sugar decreases in response. The lower blood sugar triggers tiredness and hunger. When you eat carbs and try to lose weight, you need a consistent calorie deficit to trigger even minor fat burning. Higher levels of insulin (from more carbs to process) inhibit fat burning.
When on the HCG diet,
for example, (or atkins or primal or one of the other diets that allow intermittent fasting), your body shifts away from carb-metabolism and falls into ketosis - fat burning mode. But, you need to take diet drops to control your hunger hormone. You can get diet drops from this
source, site which reviewed best hcg drops. While in ketosis, insulin levels change very little meaning energy levels are maintained even while fasting. Because you're in fat burning mode, fuel (body fat) is always available. The HCG helps maintain ketosis more easily.
I'm currently using a primal diet and I don't eat at all unless I feel actual physical hunger or during workout recovery. I have lost weight from fat and gained muscle nicely. I am very healthy.