Obviously it's period-sensitive to some degree and most applicable in late C20 warfare as taught. Although I suspect that it might not be a bad rule of thumb across various periods, given considerations of morale. If half your mates are dead, you aren't going to feel great about doing any more fighting, unless you are already up to your neck in it. I suspect that historically, a formation at 50% strength is pretty likely to rout, given half a chance.

War is not a great leveller: Junior Officers typically die faster than anyone else on the battlefield, with NCOs not too far behind in the running. Thus a 50% casualty rate will mean a high-that-that proportion of Officers and NCOs being 'absent', with a knock-on effect on cohesion and organisation. If you have half your men, but only a quarter of your C&C, things are not good.

For operational purposes, 75% is the key number: One wouldn't commit a unit that was operating below that level to any offensive action/operation, and would rotate it out-of-line if it was at all viable to do so. There's no point flogging a horse with three legs, and reserves are there for a reason.
At 50% the unit might as well not be there, and it effectively isn't worth considering on a strategic level.