Ok I want to put out there that the #1 dangerous halter that I have personally been involved with is one with a throatlatch snap. I don't know, maybe the horse had talent to do stupid things, he was in my sight, but turned around for one second and he caught the throatlatch snap on the fence, got him loose still had the halter on but had to take care of a few things after that, got it caught again, he finially had to break it, but I will say that halter was nylon and it took great deal of effort for that thing to break, and it was the snap not the nylon itself. I never really liked those halters to begin with, it came with a different horse and what I could grab at the time.
So anyways that is my choice of halter that I find most dangerou is the throatlatch snap halter. Will never, every, buy one.