I've been around a lot of wild bucks, bears -black & grizzly, a few bull elk, as well as assorted other wildlife - the only time I ever even thought I was in danger was a mountain lion I called in while elk hunting. It was stalking me and even when I waved my arms and yelled at it, it kept coming, just circling to get behind some trees. At less than 10 yards I shot at it, but the arrow hit the shoulder and glanced off the quartering to me cat - then he ran off about 30 yards, paused to look around, and with a twitch of the tail walked off up the mountain.
Never even crosses my mind that a deer would be dangerous, next we'll have to watch for meteors.