I think they outgrow stutter because they let go the worrying and the strategies about speaking. Initially, because they are learning to speak, they have to think more in order to correct themself. Because they are learning. Some parents tend to be very strict on this matter and make the correction job their hobby. (maybe that is why we have a fear of adults/autorithy). But in time the child learn the words and how to speak them on a average level so they can let go the thinking and planning. They change to just speaking by "heart". Faith speaking so to speak. But if the child never make the change of speaking consciously (controled, effort) and keep holding on to thinking and strategies to perfect speech chances are we will continue to stamble growing up. Even worse, when they get older adults will notice he/she stutter and they probably will tell them that they have a problem. Making them even more conscious of their speaking and so stuttering more. Even worse! after that you go to a speech therapist and he/she will assure you that you have bad breathing technique or you have defectous speech mechanism behaviour so you need to concentrate even more on your speaking. So there you go. +20 years of totally conscious speaking. Fully inmerse on thinking the words to existance. The opposite of natural fluency.