Is stuttering psychological or neurological?

Is stuttering psychological or neurological? What do you think it is? Some say its neurological while others say its psychological. My question is this: If it is neurological, then how have so many stutterers been able to give speeches fluently, act on stage and have conversations fluently? Surely if it is neurological, then they would not be able to control it and they wouldn't have been able to give those speeches. And I know there have been studies which show that stutterers have less blood flow to the broca part of the brain (the part responsible for language and speech processing), compared to people who don't stutter. So one might say that this abnormality is what causes an incoordination in that part of the brain of the stutterer, and that's why he/she stutters when they are conversing. If that is the case, then why is it that stutterers stutter even if they have pre-formed a sentence in their heads 1 hour before they have to say it? They already know the sentence, so the broca part of the brain doesn't have to form it. A lot of stutterers struggle with saying their own name too. Why? As for the broca thing, I think the reason stutterers have less blood flow over there is because they are not using that part of the brain as efficiently as people who don't stutter. The stutter itself is preventing that. Some stutterers claim that they can speak properly by themselves, but stutter when they talk to other people. So could it be that the problem is the not speech itself but another pressure? (social or time pressure) I know that there are some cases where its neurological. People who suffer from multiple sclerosis can develop it, but over here I'm talking about regular stutters. The kind that develops during childhood.