Some problems with neck knives:
1) You want to conceal it, the chain shows, but no big deal. (Already mentioned above)
2) Use a breakaway hanging method. If not, the bad guy can jerk your around like you were wearing a necktie, or is it a noose. (Already mentioned above.)
3) School teachers know from experience that kids can and do grab anything hanging around your neck. So they might get the knife.
4) Can you reach it? If it's hanging beneath your shirt, you may have to dress to the neck knife's limitations in order to access it quickly.
5) It swings. It is not always in the same place for reliable access.
6) No hilt or good handle. If you hit bone, your hand will slide forward and be cut. (CSI loves this story line. They always find the Perp.)
7) Small. Wont cut deep. (But hey, if you have been grabbed even a 22 short or a neck knife is better than nothing.)
8.) It is still a concealed weapon. In many states, a knife must not only be within certain size and design limitations, but it must conceivably have a use as a tool that justifies it's carry, like a pocket knife.
Some Alternatives:
a) Be alert to people and positions.
b) Carry a key chain pepper spray that fits easily into your pocket. Make it a habit to carry your keys, with spray ready, in your left (weak) hand when you exit your home, car, restaurant, anywhere.
c) Legal size, assisted-open (also legal) pocket knife clipped to your right (strong) side. (Google on Kershaw Speedsafe Blur.)
d) Your defense distance, without pulling your gun, is now 8 feet (spray a cloud in his face). And, you can pull knife or gun as appropriate or reachable. For example, R9 or even closed (assisted-open) knife hidden in right hand as suspects approach.
e) If you are surprised and grabbed with at least one hand free, you can spray, knife or shoot.
f) However, speaking to strangers from a respectable 8 foot New England distance is good advice. It’s no social mistake to move away and to the side to maintain that distance. If they follow, they have tipped their hand.