Some points on the thread.
First of all, it's good to see a decent discussion on something on this forum. That doesn't happen often enough.
I'll try to answer some of the points from Dr. Atkins and Dr. Agatston's (Southbeach) approaches.
ZNOBRDR: Yes you have to get nutrients from somewhere, that's why vitamin and mineral supplements are so important early on in the diets. You can make up those important things later on once you have gotten near the target weight and enter into Maintenance/Phase 3. Moderation is very important in both diets. You eat until you are satisfied and then STOP. You don't try and stop eating before then because you end up always hungry and then everyone except the people with the best willpower end up bingeing. That is the fate of most of the other diets out there that count calories.
MAINEIAC: Sounds like your wife's class covered the first phase of atkins called induction. That is where you cut out almost all carbs. It results in the fastest weight loss and he and the South beach diet only mandates staying on that for 2 weeks, after that you start adding in carbs slowly until you reach an equilibrium. If you have a LOT of weight to lose you can stay on induction longer but for most people you will only stay on the most restrictive phase for a couple weeks. If you go off the diet for a special occasion (traditional Christmas meal for example) you can go on induction a bit before and after to limit the impact of such carb loading, you shouldn't make a habit of it though.
FLYRYAN15: I think you have your BMI a little screwy too. You are talking about your percent body fat which is totally different. If you are 6'1" and 190 pounds your BMI is just a smidge over 25 which is considered overweight by the NIH. That is the problem with the BMI chart, it doesn't consider the level of fitness of the individual. Your typical athlete or body builder would come in on the chart as obese or morbidly obese even if their percent body fat is very low.
ALWAYS DEFERRED: You are spot on with the water. Atkins recommends drinking at least 8 12 ounce glasses of water a day (for South beach- 2 or 3 quarts, however many ounces that is). The vast majority of Americans go through life chronically dehydrated which can lead to headaches and lack of energy at one end and kidney disease and possibly cancer at the other.
Also if the class you went to is saying that about the kind of weight you are trying to lose, I wonder what diet they are talking about because it isn't atkins or south beach. What you are talking about is what can happen on a low calorie diet when you haven't regulated the amount of insulin in your system.
The whole point of the induction/phase 1 period is to get your body into the mode where it uses the weight you want it to use, lypolysis. The idea is to get your body into using ketones for fuel instead of glucose, where it is using the stored fat for energy, the only possible way to get it out of your body. The body is evolved to use that stored fat during periods of starvation, it does not imbibed protein into energy. Your body only uses its structural protein as a last resort. Blood sugars first, stored fat second, then after all that is used up, proteins. If you ran out of stored fat your body would begin burning muscle, but most americans are a LONG way from that. The great thing about being in lypolysis is that when your body processes fat for energy it converts them into ketones. When your body converts carbs to glucose for energy any excess to your imediate needs are converted to glycogen for use as an immediate source of energy stored in the liver and muscles. But there is a very limited amount of glycogen that your body can store there, the rest is all converted by the liver into fat and stored in your belly and other unappealling places. If your body is converting fat into ketones for energy it converts more than you need "right now", but unlike glucose or glycogen, the body cannot metabolize ketones back into fat. It is a one way process for our systems. Any excess ketones not immediately used are flushed out naturally in the urine.
JediNein: You are right, the diuretic effect of coffee isn't a problem. However the caffeine is a big problem. Caffeine causes a hypoglycemic reaction in your blood (low blood sugar) by stimulating the pancreas, which causes food cravings and a tendency to overeat. If you can eliminate it great, but at least moderate it to one or two cups a day. Both South Beach and Atkins recommend that if you need caffeine, tea is a better choice. There is lots of evidence that tea can a beneficial role in the prevention of heart disease and prostate cancer.
SaladShooter: The Atkins and South Beach diet are all about changing your lifestyle, that's why there are several phases after the first one. The idea is to get you to a point of balance in your system where you can enjoy what you eat and maintain a steady, healthy weight. The idea in both diets is to take advantage of the metabolic benefit of burning fat instead of the simple sugars. At the end of both diets you are eating a wide variety of foods like most vegtables, fruits, lean meats and even whole grain foods like pastas and some breads. You have more energy so want to get out more for exercise and not sleep as much.
To everyone: All I can really say is that this diet is working great for me. I was doing the low-fat thing for a while and it wasn't working. This diet has been relatively painless. I enjoy the variety of foods I can eat and its only getting better with food companies recognizing the market for low carb. The benefits I enjoyed were immediate. I have more energy, I'm not crashing in the middle of the day anymore and countering it with caffeine and a candy bar. I feel better, no more headaches from caffeine withdrawal or low blood sugar. I've lost 25 pounds since October and am wearing pants I haven't fit in since I left the army. I'm don't have hunger cravings anymore and the sweet tooth I've always suffered from is gone. I haven't gotten to my target weight yet, I have a bit more to go, but for once I'm confident that I can get there and stay there.