No, stuttering isn't copied either - it's not contagious. Neuroplasticity is not relevant here. You have to be careful that you don't think in terms of advanced concepts, that you don't apply properly. I'd say it's important to your self-understanding that you start thinking about stutter in different terms. Don't invent theories. Leave that to the actual scientists - and do by all means seek out what can be said scientifically about stutter, based on the research that's been done so far. - However - you're right that we can fear stuttering. But we can also work on that kind of fear. Have you sought out help in this regard so far?