I used to do it. I did it because on some level, whether I thought it was Big or small, I was trying to hide my shame. At first I didn't it shame because I was okay auditorily showing stuttering, but I didn't want to look "weird" and therefore hid that part which felt more shameful. Eventually through good and intentional therapy, I stop hiding and no longer cover my mouth when I stutter. But I also worked on reducing my reactivity/secondary behaviors as well.