What DJ_Jestar said ^
More simply put:
Building muscle requires a surplus of calories. (more than your body needs to maintain current weight)
Loosing weight/burning fat requires a defecit (less than your body needs to maintain current weight)
It's a catch 22. It is possible but is very difficult. With exact diet and correct training it's possible put for a lot of beginners and even intermediate trainers it's tough.
Why can people miss the completely obvious time, and time and time again.
If you're eating say 3k calories and losing no weight, and drop your INTAKE of calories to 2k calories a day and start losing weight. Its not magic, your overal calorie use is STILL 3K, you are just using body fat as an alternate source for energy.
Building muscle, exercising and eating protein will/can cause your body to use extra energy to do so, losing weight causes your body to use body fat as an energy source, theres no catch 22, its perfect.
If you're a stone overweight, you have 49000 excess calories available to fuel your body. These aren't ignored, your body uses them.
If your body is capable of accessing the body fat easily, metabolising it into energy, your body can use it.
Eating 2k calories, made up of mainly protein, good fats, few carbs, and enough vitamins and minerals to allow your body to consistantly burn body fat, then having your body burn off 1000k calories from internal fat source, would be the same as eatig 3k "normal" calories on a normal diet.
Someone losing weight and eating 1000 calories is NOT USING 1000 calories.
Building muscle while burning fat is rather easy, but as with all things, diminishing returns occur. If 100% is the "normal" amount of muscle your body should have, then if you have 80%, building up to 100% is easy, if you already have 120% of the muscle you have, its very hard to gain more muscle. So someone at almost their peak will find losing weight and gaining muscle hard, purely because they'd find gaining muscle alone pretty hard.
The catch 22 part of the equation is this. A "normal" diet doesn't require your body to burn excess body fat in anything but minimal quantities. A normal diet won't have the necessary intake of the minerals and vitamins to fuel the body fat burning process indefinately because, why would it?
IE if a normal diet only has enough b-vits, and everything else used to metabolise fats, to burn a few hundred calories of body fat, why would anyone expect when you reduce your normal diet, to have enough b-vits and everything else, to burn 4-5 times the normal amount of body fat used in a day, it makes no sense and is simply ignored by people.
This is the fundamental problem and why so many people lose fat slowly, your body doesn't just say "need more energy, burn all the fat", the body is a complex system and burning fat does NOT happen on its own, the body uses, essentially catalysts to turn fat/carbs/protein into energy, if you don't have any of the catalyst left, you can't burn fat, its really that simple.
The key with losing weight is simply dropping your intake of food, and providing your body with the ingredients it needs to use body fat as a continual food source.
I'm over simplifying it but, assuming on a 3k calorie diet you can't lose weight, and in that diet you get 500mg of b-vits(and for the sake of argument assume thats all thats required to turn fat into usable energy). Now that 500mg's is used to produce 200 calories of energy from fat.
Now you reduce your diet to 2kcalories, your b-vit intake goes down to 333mg, which can now only burn 133 calories of fat.......... you actually wanted your body to increase its fat burning by 1000 calories?
Muscle needs a few things to be built, protein, energy, water, various minerals and vitamins. Again if you say need 500mg of b-vits to build 10grams of muscle, you reduce your calorie intake, your body only has enough b-vit to build 6.66grams of muscle.
Protein's not really an issue, eat as much as you want, if you're building muscle and your body has the building blocks to do so, it won't be used as energy. Vit's/minerals, on a smaller intake of food, you will still want an increase of vits/minerals to build more muscle than usual.
Energy, as said, if you're a stone overweight, you have 49k calories spare on your body to fuel muscle building.