BEagle - its not good enough if you have a student who presses you for further explanation.
So peel the onion by another layer. BEagle's explanation is perfectly robust to that:
Explain why the angle of bank causes the C of G of the aircraft to start moving in a direction at an angle to its longitudinal axis: roll -> bank -> slip
Now explain why moving in a direction at an angle to its longitudinal axis causes yaw: slip -> yaw
It really is that simple.
If you roll with back pressure applied as you should, do you get yaw (without using rudder)?
Yes, of course you do.