* A "live" ANC process has no control over the environment from which it receives the audio signals that it acts adversarially against.
* When transmitting audio waves from one medium to another, there will be latency. Perhaps not much, but it will be there.
If you accept these two positions, then consider this:
* What happens when a sound wave that is being combatted (via phase inversion) suddenly stops, or inverts it's own phase? That's right, ANC could potentially double the amplitude of the frequency being combatted.
* I imagine that ANC technology takes advantage of latency to ensure that they don't damage people's hearing, but the nature of ANC requires low latency in general, otherwise you can't be sure that you are combatting the correct frequency (at which point you risk doubling the amplitude due to abrupt changes) - if someone more familiar with the actual algorithms could chime and correct me I will happily stand corrected :)