It isn’t impossible, idk what these people are talking about. Considering a stutter, for a lot of us, is something that we’ve nurtured and created ourselves whether we accept it or not, it is possible to become influenced by the way stutterers hesitate, prolong, and block, and pick up those habits themselves. So while a stutter isn’t contagious, you can be influenced by the way a stutterer speaks, just like how non stutterers can be influenced by the way other non stutterers speak.