I've never seen an electric hand drill with a tapered chuck. I'd truely be interested in seeing a pic of that drill. If it actually is a taper, then there should be slot in the spindle where to insert a wedge and that should just require a few taps to break the friction bond.
I don't know if that's true. IMO if it's a tapered chuck it would be more like a JT33 taper. MT, such as on a drill press would be as you described.
Had he given a model # we could have looked it up.