Of course they won't. Carbs are a habit as much as anything else: we
like to see a nice, full plate of food and when we see an emptier plate, we're instantly thinking of dessert or supper before bedtime. Just like smokers can quit the cigs but miss the habit, so it is with carbs.
Maybe the OP
will continue to eat the massive stilton wheel - and more power to him. Both the first time I went LCHF and this time I've started now, I must have eaten around 30 Peperami's in a week. That's just how it goes. Eat mindfully, enjoy it, then move on.
The Fat Emperor thing is also correct - it's the actual "What happens" when we're fat adapted. A lot of it is a bit nonsensical (bodies be weird machines, eh?) but that's mostly because the guy's an engineer who specialises in processing information into models. But he's an interesting chap and if you can give yourself a bit of time to listen to one of his talks, you'll see he's a genuine fellow with a lot of really sound, up-to-the-minute sources feeding his information:
http://www.thefatemperor.com/latest-material/
In essence (though not universally), if we've managed to persuade our bodies to burn fat for fuel, our bodies aren't going to be burning AND storing the same stuff. SO what doesn't get burned gets thrown out because, guess what? There's another meal on its way and still no carbs. And we turn that fat into all kinds of interesting and fun stuff in order to get rid of it. But, the term for getting it out of the body is, exactly, "excretion" - it's not just a poop word!
You're right to be confused. It IS confusing, and it's the big diet secret that every single self-help diet book of the last 30 years, every slimming club, every nutritionist and dietician has been keeping from you. Given that you've had to stumble onto the info yourself - in the face of a lifetime of not-quite-accurate information, it's completely natural to be skeptical.
Enjoy your food. Eat without guilt. Be healthier and happier. I wish this for everyone x