How have you ruled out other explanations for instinctual behavior? For example, there is a body of scientific work which offers evidence that instincts are passed down through genetics, a mechanism which doesn't require that the brain be deterministic. What are the scientists studying this area getting wrong?
What about twins that are separated at birth but grow up to be different? It seems that the existence of even one such pair of twins would invalidate your claims, given how fundamental this would be to the operation of the brain.