Possibly you do not understand the the spatial effects of listening on headphones. When you listen on speakers both of your ears hear both channels. Your right ear hears a lot of the right channel and a bit of the left, and vice versa. So, assuming the musical event was recorded with the classic two microphone positionings, you will hear something that approximates to that event.
If you listen on headphones where the right channel goes into the right ear and the left channel into the left and there is no mixing in your pre-amp or 'dummy head' processing, you will still hear stereo but the channel separation will not be the width of your head, rather it will approximate to infinity since each ear hears only one channel. Of course, this gives an entirely different spatial presentation. One that I have enjoyed but is not classical stereo.