He asked me to show an ID, I asked "why?", and he just responded "Because I say so". I was a bit too flabbergasted and not prepared for that answer and just showed him. He then proceeded to someone else who was even requested to come to the counter and let his bags get checked.
I'm curious whether I was actually required to do so.
I see no reason why it is any of the cops business to know who I am when I'm just walking down the street.
Same situation applies at the border, there is a seperate section for Schengen countries in the Amsterdam airport and you normally get in and out without showing an ID. I see no reason why it suddenly is any business to the customs officer to see who I am.
However, in every airport where I've seen that, I've certainly been able to get as far as the gate without ID (particularly if I've a pre-printed boarding pass), but I've always needed either a passport or EU member state ID card to actually get on the plane.
If you can get on without your ID, however, there are generally no checks at all at the far end.