My answer isn’t scientific but just a matter of what I have been told by my speech therapist. So, if anyone has a more scientific answer, please do let us know. My speech therapist says that lowering your voice decrease the air flow through the larynx and there is less resistance to the vocal cords making it less likely to stiffen like what happens when we stutter. So, when you raise your voice, there is more air flow going from your lungs and through your larynx that puts stress on your vocal cords and causes the spasm and hence the stutter.