Instructors are sometimes from the old hard cowboy gene-pool ... On many ANR headsets the passive dampening, when power is cut off, is less then a standard passive headset could provide. Some older instructors therefore prefer passive headsets, because they don't have to think of carrying batteries for the ANR - as training machines usually have only standard plugs without integrated power supply.
As a private pilot you either fly less then an instructor, so batteries are not such big issue, or frequently use a plane where power supply for the headset may be available. If you own a plane, most probably you add the headset power supply very quickly ;-) as ANR is a big advantage.