I've been told by an "expert" that Noise cancelling headsets that create white noise can cause permanent damage to your Ears if you use them too much?
Not a pilot, am a retired electrical engineer, and a serious amateur audio guy.
If you amplified the white noise NC headsets produce high enough, of course it could damage your hearing. Also true if you amplified the sound of a baby breathing high enough.
But that white noise is not the way they cancel noise, but a result of imperfections in the the implementation. The moderate amounts I've heard are likely no more harmful at equal level than cabin noise from the engines. And, as in fact lower level, less harmful.
You badly need a new expert.