Stammering is not a disease. It is just a bad habit. Old habits die hard, but if your willpower is strong enough, you can change your habits with practice at any point in your lifetime. You can also change your bad habits by practice. It is just because high speed, short breath and pshychology due to following reasons.
Physical weakness due to some illness. Some fear. Imitating a stammerer. Accident or some mis-happening. While playing, children talk with each other very much. Due to lack of breath, a person starts speaking with pauses and interruptions (as speech develops from breath). But, he does not want to speak with breaks. Since he is not aware of the actual cause of these interruptions, he tries to speak more words in that short breath. The result is an abnormal increase in the speed of speech. Trying to speak more in a short breath causes stammering and this becomes a habit. This precisely is the concept of stammering.