Well put it that way - there are carbs and there are carbs. Complex carbohydrates do not equal simple carbohydrates.
Carbs get a lot of bad press, but really if you eat complex carbs (brown rice, brown bread etc), then you can eat a fair amount. Simple carbs such as sugar, honey, white bread, pastries etc should be kept to a minimum.
Carbohydrates range from 1 simple molecule of sugar (glucose), to very complex macromolecules made of lots of glucose (such as starch, or even cellulose like plant leaves, which we cannot diggest). Glucose is the body's prime source of fuel. Your body needs to keep a fairly constant concentration of blood glucose for it to be used up as energy during respiration by the brain, muscles etc. When you eat a simple carb, they are absorbed very easily by the gut, so suddenly your blood is overloaded with excess glucose, which needs to be stored away, and your body does that by releasing insulin. Not long after, you're likely to be hungry again. When you eat a complex carb, it needs to be cut down into simpler forms (ie glucose), which takes a long time as it requires a lot of enzymes etc during digestion. This leads to the slow release of glucose in the blood, maintaining blood glucose levels, and keeping hunger at bay.
Fat is also essential - in fact too little fat in the diet is dangerous. However once again, not all fats are equal. Fatty acids (omega fats from fatty fish and nuts), mono and polyunsaturated fats are the good ones. Trans fats (do not occur in nature) and saturated fats are not good as they tend to "stick" in the arteries.
Protein of course is essential too. Excess protein and low carb leads to ketosis (the principle of Atkins - most of the initial weight loss is due to water loss) which in the long run can strain your liver and kidneys as proteins are very costly for the body to deal with, as well as bad breath.
If you have a varied diet with the recommended daily allowance for fat for someone of your age, activity level and gender (usually max 70g for a female), and if you eat enough protein (most people do - aim for approx 0.7g per kg or 2.2lb), then you can easily eat complex carbs for the rest!
Historically and traditionally, humans have always eaten a lot of carbs, up to 70% of their total calorie intake. As long as fat and protein levels are kept to a reasonable amount, then the rest can be eaten as complex carbs without any ill effect. "The Evil Carbs" is a recent invention - people were a lot slimmer in the past and heavily reliant on them - no Atkins, low carb or fancy protein bars! The real problem lies in simple/refined carbs and fatty food that are inundating us. The slimmest populations in the world, such as the chinese, eat a lot of carbohydrates.
You have to find something that works for you - don't be scared of the good carbs. Keep your fat levels to a healthy amount, eat enough calories per day, and try to balance your carb/protein ratio (I'm against low carb as you can prob tell, so I'd say eat more good carbs than protein).