In case one, the person intends to do neutral observation of their breathing, notices that their involuntary breathing has changed in some hard-to-define way as the result of observation, and, as far as I can tell, typically decides that meditation is too hard for them and gives up.

One person I've talked with about this also mentioned that observing her breathing also caused her to become anxious.

In the second case, observation disrupts involuntary breathing completely, and breathing has to be done voluntarily until attention drifts away to something else. People with this problem seem to stay with meditation longer, but I don't know if the problem is ever resolved.