Most scientists who study stuttering have maintained that stuttering is a neurodevelopmental disorder, meaning that it is caused by misfiring or reduced activity in certain areas of the brain. It's framed as more of a physiological issue, relating to things happening with the parts of the body itself (this case the brain) than psychological. Saying this, there are cases of psychogenic stuttering caused by extreme trauma or stress. There's also a lot of other causes of stuttering that doesn't have anything to do with the psychological or developmenal state of the stutterer, such as a stutter that may manifest with a traumatic brain injury. Brain research is still in its infancy and for anyone to make a broad statement that speech issues are only psychological isn't doing the science behind it justice. To say that all people who stutter have psychological issues ignores that with some stutterers it's not how they feel or what's happens to them that causes their disflunecy but how their brain works. It also pathologizes people who stutter and frames it as a mental disorder (you stutter, so you're crazy) when, again, in some people it's just a thing their brain does. The DSM-5 does include neurodevelopmental stuttering as a "mental disorder" because of its comodities of extreme anxiety and avoidance and so speech therapy (which could lessen the anxiety that comes with anticipation of stuttering by learning fluency-enhancing skills) could be covered by health insurance. I don't know how long it's been considered a psychological disorder by the VA, so I can't give any insight there.