Burning fat and gaining muscle over the same time period is called body recomposition.
If you search on that term you will come up with a lot of hits.
Recent studies continue to show subjects gaining muscle and losing fat simultaneously.
This includes both men and women, and all age groups.
It's not even a question of dispute anymore.
Body recomposition is real.
However, and here is the catch - it's difficult and it occurs most often in beginners.
These are the people who have just started lifting.
Beginners gain muscle much much more easily.
The longer you've been training and the closer you are to your genetic potential for muscle growth, the harder it is to gain more muscle.
And the less likely it will be that you'll gain muscle and lose fat at the same time.
Body recomposition is usually achieved in people who have average or above-average body fat.
The leaner you are, the less likely it is that you'll achieve great results in body recomposition.
When you are lean your body is far more likely to lose muscle in a deficit.
On the other hand, gaining muscle when you're lean and in a caloric deficit is very difficult.
A situation where body recomposition is often successful is in someone who built a significant amount of muscle but stopped training for a long period of time.
If someone had a lot of muscle then lost it, its easier to rebuild it due to muscle memory and body recomposition is more likely.
To sum it up, the best way to achieve body recomposition is to use a calorie cycling strategy where about half your days are in small surplus and half are in small deficit.
The ideal way to go about this is to eat in surplus on hardest training days and eat in deficit on rest days or lower intensity resistance training days.
If you look at it this way the muscle gain and fat loss are indeed not happening simultaneously.
Instead, you are alternating between periods of deficit and surplus and the net result is more fat and less muscle.
Another option is to simply stay in a very small calorie deficit and train extremely hard with progressive overload.
Ideally, it's best to focus on one goal or the other.
Focusing on fat loss or muscle gain at one time is more efficient.
Again, it really is possible to achieve body recomposition.
It's just hard to do and not everyone can do it if they are already well-trained, close to genetic potential, and lean.
Alternating between long phases of building and cutting is still the standard best practice.
If someone gains muscle while in a cutting phase, its looked at as a nice bonus.