Every process that happens does so at a sub-atomic level, even the process of putting food into your mouth. But that process is much more easily understood with the concepts food and mouth than trying to explain it with quantum physics.
When it comes to the brain, however, there isn't really a good explanation on the macro-cosmic level of what the process of thinking involves, which is why scientists are looking into descriptions involving quantum-physics, on a sub-atomic level.
Just because we understand something a certain way doesn't mean it cannot be explained in another way. Everything involves waves and particles, even though describing something in those terms isn't always the most practical.
In a way, classical physics can be thought of as the physics of our perception.