Since the fraying cable is not sliding within a casing at the frayed spot the fray only is a long tern safety thing. Now if the cable had rust of damage where it did slide in the casing that would be a brake arm moving issue. The base reason why one canti won't retract back from the rim like the other side does is some thing between the two sides is not equal/balanced. One pivot having more grit/rust causing more friction. One spring being weaker than the other. One pad installed far in along the shaft and the other pad at the outer end so the geometry is off. The wheel isn't centered. One side of the straddle cable is longer than the other half. BTW these Shimano like straddle cables can be installed incorrectly (They are a safer design compared to the continuous canti end to canti end types).

I see one pad positioned near the top of the canti arm's slot and the other closer to the slot's bottom. Can you position them so the are mirrors of each other angle wise? If the pad's faces are work at an angle that won't mate with the rim you can file/grind the pad's face flatter. Andy