Why is the homolytic cleavage of the breaking bond drawn with a 'fish-hook' arrow?
Homolytic cleavage uses a fish-hook arrow to show the movement of single electrons during the breaking of the bond.
Fish-hook arrows also indicate the motion of single electrons during the formation of a bond.
The fish-hook arrow distinguishes one-electron movement from two-electron movement.
Heterolytic cleavage involves the movement of two electrons at a time.
Here’s a video on the use of fish-hook arrows in homolytic reactions.