We know that people who stutter often show variability in their stuttering, and this is sometimes related to internal as well as external factors. Sometimes, for young children, disruption of routine, fatigue, or any excitement or arousal state can lead to increased stuttering. What is very important to note is that these things do not cause the stuttering to begin in the first place. That is, they may exacerbate or make worse an already existing stuttering problem. That is why, for young children who stutter, therapy usually involves analyzing the environment and the child's reaction to the environment to see what factors may lead to increased stuttering and which may lead to increased fluency.
Some children react well to reduced time pressure in their daily routine.
That is, they may actually speak more fluently if the tempo of daily life and scheduling of their daily lives is slowed. That doesn't mean that busy schedules cause stuttering, and it doesn't mean that things like anxiety cause stuttering. If that were the case, most of us would have stuttering problems. While slowing down may help young children to speak more fluently, speaking quickly does not cause stuttering. The answer is that it is a problem with speech.