Because they are not speaking with one voice. One part of them wants to say what they are trying to say, and another part of them doesn't want to say it, and it therefore comes up out haltingly--in the form of a stutter, in other words.
Stuttering is not confined to speech. People take 'stutter steps', meaning that they half-act, instead of acting whole-heartedly, and literal stuttering is really just a specialized form of the broader phenomenon of equivocal action.
Beware of stutterers. They are lying to themselves and therefore to you as well.