Coming around a bend on a bike path -- I don't normally ride bike paths except to get to places most easily reached by the bike path -- I had to turn wide to avoid an oncoming cyclist on a hybrid who came wide into the turn. I'm generally pretty good at judging that kind of thing at speed, but I hadn't accounted for his rearview mirror sticking out about 10 cm from the left side of his handlebar. That brushed my sleeve. If I'd been off by one more centimetre, it would have caught my arm and I would have been pitched over a bridge into the Lachine Canal.
Mirror are a menace. Use your neck.