Why do airplanes start descending when we initiate a left turn?
This is because when you roll left (or right), the lift changes from pushing up to pushing up + left. This is what makes you turn. Since some of that lift is being used to the left, not as much is pushing up, causing the plane to lose a bit of altitude. On FlyByWire aircraft, since it is computer controlled, the computer automatically compensates for this by adjusting elevators to pitch up slightly.