I'm not blaming Atkins for this, but I think he undershot and then overshot his carbs. The induction ketosis phase was too low carb for most people, and the later phases were too high carb and approached CW. It was hard to stick to, and was legitimately attacked for being dangerously low-carb. The Atkins phases missed the Primal permanent ~80-120g carb sweet spot. The fake food business angle didn't help either.
Sample answer to OP: "Primal/Paleo is an evolved () version of the original 1972 Atkins. After more research, we've learned from the mistakes of the original Atkins. Paleo/Primal is lower carb than the government recommendations, but still has enough carb from veggies to fill your body's needs. Eating Primally is easier to stick to, doesn't rely on pre-packaged foods, and works."
And that's when you pull up your shirt and show off your weight loss and/or six pack and tell them to go pound Himalayan pink salt.
5'0" female, 44 years old. Started Primal October 31, 2011, at a skinny fat 111.5 lbs. Low weight: 99.5 lb on a fast. Gained back to 111 on sugar cheat. Currently fighting off sugar/candy cravings with bulletproof cocoa and a little rice.
I (try to) follow by-the-book primal as advocated by Mark Sisson, except for whey powder and a bit of cream. I advocate a two-month strict adjustment for newbies. But everybody is different and should tweak Primal to their own needs.