Why does wing bending cause wingtip twisting?
I would say it's because the twist in question relates to Mean Aerodynamic Chord, which is always aligned with the longitudinal axis and airflow, and diverges from the airfoil chord line when the wing is swept (it becomes a truncated slice you might say).  

Assume a wing that can bend along its spar axis but that has perfect torsional stiffness for our purposes.  When a straight wing is bent up, the incidence of the MAC at any given point, being perpendicular to the bending axis and the same as the airfoil chord, remains the same from root to tip. 

On a swept wing that is bent up, the airfoil chord line, perpendicular to the span wise center line (B), also remains untwisted along its bending axis (in our perfectly torsionally stiff wing), but the MAC, which is now different from the airfoil chord line because it's aligned with the longitudinal axis (A), sees a geometric reduction in incidence in proportion to the bend.