Yeah, apparently it's a thing that many stutterers tend to do. I wasn't aware of doing it, but when I was informed that I did so, it suddenly became more awkward to carry out a conversation. These days, I've sort of found my own balance for it. I think it appears more as a trait of my personality now, rather than avoidance. It's just become part of how I communicate. Besides, non-stutterers don't fixate their eyes constantly. But yeah, we do have to look sometimes. It's preferable (and helps establish a better rapport with our conversations partners).