Stuttering is a neurological defect first and foremost. This means that somewhere in our brain the wires are crossed up, which leads to us not being able to translate thought into speech as effortlessly as most people do it. There is no physical trait which causes stuttering. However, the neurological defect manifests itself through physical means (through our speech muscles). Our speech muscles don't act the same as a fluent person's will when we stutter...there's a neuron misfire occurring somewhere in the process from brain to mouth. So it's kind of both physical and neurological from that perspective. This is the heart of most speech therapy techniques. If we can teach out muscles through trial and error to act the "right" way when we speak, then what we are actually doing is reinforcing the neural pathways that are used to form those sounds. More reinforcement, in theory, should train out muscles to form sounds correctly. Of course it's not always that easy, buy that's the thought process behind it.