I remember the instructors in Basic and AIT screaming that the M-16 did not have a MF'ing carry handle, that it was a rear sight housing. Those that chose to use it that way were vigorously and physically corrected. There was a strong emphasis on muzzle awareness and not flagging each other. To this day I find it difficult to hold any rifle in a similar fashion.
I was going to say much the same thing. We even had a rifle (the L1A1) fitted with what was undeniably a carrying handle, but woe betide you if you were ever seen to carry it that way. Even decades later the idea of carrying a rifle like that (or on a sling, unless doing something which requires both hands) goes right against the grain.
