What makes you say noise cancelling headphones are bad? Are you talking about audio quality, or bad for your hearing?

No. You're going to have to expand on that. Active noise cancelling means there is less sound reaching your ears. It works by -- quite literally -- cancelling the sound waves.

Insert "now you're thinking" meme image:

Sound can't hurt your ears

If it doesn't exist

Active noise canceling adds sound pressure. It doesn’t stop outside sound, it adds an inverse sound to prevent your perception of sound.

You do not know of what you speak. It does not add sound pressure. Reducing sound pressure is the physical mechanism by which it operates. The inverse sound means that both sounds literally no longer exist.

> prevent your perception of sound.

No. It is destructively interfering with the wave. You don't perceive it because there is no more sound, not because of some perceptual trick.

(For any pedants looking on, I'm ignoring the fact that the cancellation may be imperfect. Unless there's actually constructive interference going on -- which is not what delinka is saying -- there is plain and simply less sound.)

Of course it will affect air pressure, but in theory it should be literally cancelling the sound waves. All the literature I can find at a cursory glance suggests ANC headphones are better for your hearing.

ANC isn’t perfect. ANC leaves a noticeable low level of noise from imperfect sensing, processing, and cancellation. It’s quite easy to imagine that this could be detrimental (as compared to passive noise canceling).

It’s probably not as good for your hearing as an equivalent level of passive NR. When I fly long trips, I notice that my hearing is slightly impaired for a day or so. There could be a lot of confounding factors there, of course.

> leaves a noticeable low level of noise

That's not added sound, though, that's a portion of the original sound that just didn't get cancelled.

The likelihood that it’s 100.0% original sound and 0.0% imperfect opposing waves is extraordinarily low.