It's simple. Carbs? no. And it also turns out it's very, very difficult to overeat if you avoid carbs entirely.
If you avoid carbs entirely, you're going to be incredibly unhealthy. Carbs include vegetables, fruit, and are the primary calorie source in most legumes.
Incredibly unhealthy?
I can eat vitamins or even low carb vegetables/fruits and get all the nutrients I need even if I actively avoid carbs throughout the rest of my life.
Manufactured vitamins are a (very) poor substitute for following a proper diet. There are problems with regulation of the whole supplement industry. There are problems with bio-availability of many of the nutrients in pill form. There is the lack of the different types of fiber, which study after study have been showing is a vital component to good dietary health.
If you're eating lots of carbs via vegetables and fruits you can totally have a healthy diet. That's kinda a no-brainer. You said "Carbs? no." and "avoid carbs entirely" though. That's extremely unhealthy advice, and would involve cutting all vegetables, fruit, and legumes out of your diet.
I think that what you mean to say is "avoid eating empty carbs". Energy without fiber and nutrients . . . like most white breads, white rice, white pasta, most things with pumped up amounts of sugar (cakes, cookies, crackers, pretzels, etc.). If you primarily eat fried chicken and beef jerky, cutting protein from your diet for a period of time will improve your health. That's not because protein is bad for you, it's because you've been eating eating shit protein. By the same token, there's absolutely nothing wrong with carbs (they're essential to a healthy diet) . . . just don't eat shit carbs.
(I'd actually argue that there's a place for a certain quantity of high glycemic index very digestible carbs in a properly designed dietary plan for an athlete . . . but that's a whole other can of worms.)